
Class 13 r f3 J 
Book J? & 



The Growth of Intelligence 



A DISSERTATION 

Presented to the 

Faculty of Princeton University 

In Candidacy for the Degree of 

Doctor of Philosophy 



by 
EDGAR A. DOLL 



PRINCETON: 

PRINCETON UNIVERSITY PRESS 

1920 



The Growth of Intelligence 



A DISSERTATION 

Presented to the 

Faculty of Princeton University 

In Candidacy for the Degree of 

Doctor of Philosophy 



by 



\* 



EDGAR A? DOLL 



PRINCETON: 

PRINCETON UNIVERSITY PRESS 

1920 



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ACKNOWLEDGMENTS 

This study has been in progress since 1909. Undertaken origi- 
nally by Dr. Henry H. Goddard, then Director of Research at 
The Training School at Vineland, N. J., it has since 1912 been 
carried forward under the immediate direction of the present 
author. The principal experimental data have been collected by 
a corps of conscientious colleagues and assistants under the gen- 
eral direction of Dr. Goddard. The analysis of these results 
was the principal research problem of the writer while a member 
of the Research Staff of The Training School. Final presenta- 
tion was necessarily postponed until the present because of the 
unusually intricate and detailed nature of the material, necessi- 
tating numerous by-studies and long-continued re-examining. 
Preliminary reports on special aspects of the data have been pre- 
viously published as "Notes" and as minor research studies. 

I am indebted to Dr. Goddard for his original work on the 
material and for his keen interest and advice in formulating the 
problems and suggesting modes of treatment. I am also in- 
debted to Mr. E. R. Johnstone, Superintendent of The Training 
School, for permission to use the material for publication. Dr. 
S. D. Porteus, the present Director of Research, has cordially 
assisted me by furnishing recent re-examinations designed to 
bring the material up to date, and by supplying me with certain 
otherwise inaccessible materials, information and references. 

I am deeply indebted to Prof. Howard C. Warren for the 
present opportunity to present the results of the study. His 
appreciative interest and helpful suggestions overcame the final 
material and technical obstacles to publication. I am specifically 
grateful to him for assistance in formulating the objective rules 
for scoring incomplete examinations, thus overcoming a serious 
technical error in the material. Prof. H. C. McComas also gave 
valued suggestions regarding the organizing of the material and 
in suggesting modifications of presentation. 



iv ACKNOWLEDGMENTS 

In particular I received constant material assistance from my 
wife in preparing the material. Her steady encouragement, also, 
in the tedium of so protracted an investigation and her intimate 
appreciation of the difficulties encountered have served to dissi- 
pate frequent misgivings as to the outcome. 

Edgar A. Doll. 
Princeton, N. J., 
March, 1920. 



TABLE OF CONTENTS 

PAGE 

I. Theoretical considerations ..... i 

The nature of intelligence. 
Intelligence and intellect. 
The course of intellectual growth. 
Average normal mental growth. 
Subnormal growth of intelligence. 
Age of arrest for subnormals. 
The rate of growth for subnormals. 
Supernormal growth of intelligence. 

II. Experimental investigation ..... 24 

A. Feeble-minded growth. 

History of the experimental data. 

Description of data. 

Correction of incomplete examinations. 

Objective rules for completing incomplete examinations. 

Treatment of original material. 

Tabulation of data. 

Cumulative mental age increases. 

Rate of mental age increase. 

Results. 

Relation of age of arrest to level of arrest. 

Rate of development. 

Relation of rate to life age. 

Rate of growth of "improving" subjects. 

Average growth curves of the feeble-minded. 

Causative factors. 

B. Superior mental growth ..... 79 

Re-tests of superior children. 



vi TABLE OF CONTENTS 

PAGE 

III. Critique of the I.Q. 85 

Constancy of the I.Q. 
Literature on the constancy of the I.Q. 
Significance of I.Q. changes. 
Refutation of the constancy of the I.Q. 
Individual irregularity of development. 
The I.Q. and the scale of measurement 

IV. Summary and conclusions . . . . .127 
V. Bibliography . . . . . . .129 



I. THEORETICAL CONSIDERATIONS 

Psychologists have tended to avoid a thorough analytical dis- 
cussion of the growth of intelligence. One finds an obvious lack 
in psychological theory when one searches for hypotheses re- 
garding individual differences in the growth of intelligence. The 
present study aims to formulate certain principles of intellectual 
growth on the basis of experimental inquiry into certain more 
or less generally accepted theories. 

The nativre of intelligence. — A serious obstacle is met at the 
outset when one attempts to define intelligence. The hey-day of 
faculty psychology is not yet sufficiently distant for us to have 
become completely freed from its influences. We do indeed as- 
sert that mind is a unity, but our text-books bear witness that we 
not only retain the faculty concepts but persistently employ them. 
Specific mental 'faculties' still flourish as 'mental functions,' 
or 'mental processes.' Even when such faculty concepts as as- 
sociation, memory, or discrimination are regarded as only differ- 
ent aspects of a unit mind they are commonly considered as parts 
of a mental mosaic rather than as different forms of a plastic 
whole. 

In our own day even if one escapes the pitfalls of mental 
processes one still feels obliged to acknowledge the traditional 
distinctions of intelligence, feeling and will. The distinctions, 
to be sure, become daily less obvious, yet even the most ardent of 
the advocates of intelligence as the fundamental mental process 
persist in keeping the distinction. 

Since Binet, however, there has been a marked tendency to 
yield the palm to intelligence as the most significant aspect of 
total mentality. The emotional and volitional aspects are not 
lost sight of, but are rather clearly differentiated from the in- 
tellectual aspects. The mental processes as units are by some 
made much of as the analytical component parts of the intelli- 
gence. By others they are ignored as an intangible complex 
which makes the whole but cannot distinctly be set off from it. 



2 EDGAR A. DOLL 

We purpose to avoid the philosophical and psychological ques- 
tions involved in these different points of view. We shall as- 
sume such a fairly clear separation of emotion and will from in- 
telligence as is commonly accepted by psychologists of our day. 
We shall also avoid the argument regarding intellectual mental 
processes and content ourself with a somewhat cursory review 
of the standpoints of the recognized authorities. 

Spearman (19) 1 believes there are two factors in every intel- 
lectual reaction, (1) a general factor (the general intelligence, 
otherwise undefined except by physiological analogy) which per- 
vades all intellectual reactions in greater or less degree, and 
(2) a specific factor (in terms of the elements of structural psy- 
chology) which characterizes the particular nature of a given in- 
tellectual reaction. 

A clear view for practical purposes is that of Binet and Simon 
(2, 3). They view intellectual action as a complex function. 
They say (2, p. 42) : 

"It seems to us that in intelligence there is a fundamental fac- 
ulty, the alteration or the lack of which is of the utmost im- 
portance for practical life. This faculty is judgment, otherwise 
called good sense, practical sense, initiative, the faculty of adap- 
ting one's self to circumstances. To judge well, to comprehend 
well, to reason well, these are the essential activities of intelli- 
gence. A person may be a moron or an imbecile if he is lacking 
in judgment; but with good judgment he can never be either. 
Indeed the rest of the psychology of intelligence seems of little 
importance in comparison with judgment." 

Specific mental processes such as perception or discrimination 
are for Binet and Simon 'phenomena of intelligence.' 

In a later study Binet and Simon analyze the 'thought process' 
or the modus operandi of intelligence into three essential ele- 
ments (3, pp. 130-155). In the course of a remarkable discus- 
sion on the nature of thinking they say (p. 136) : "Thought, as 
we believe, is composed of three distinct elements; a direction, 
an adaptation, and a criticism," and they follow this with an ex- 

1 Numbers in parenthesis refer to bibliography. 



THE GROWTH OF INTELLIGENCE 3 

position which is as yet unrivalled in keenness of insight and 
clearness of presentation. 

To these views we may add another distinctive feature of in- 
telligence which is commonly accepted, namely the concept of 
intelligence as a capacity, which is relatively independent of 
specific abilities. This capacity is considered in relation to rela- 
tively new or unaccustomed situations. As a capacity it is con- 
sidered to be innate rather than acquired, is modified more by 
heredity than by environment, is relatively unaffected by educa- 
tion except as education facilitates normal function of the ca- 
pacity, is relatively independent of acquisitions except as these 
are symptoms of the capacity, and is subject to significant modi- 
fications only indirectly through forces which favor or hinder 
mental and physical growth through the physiological mechan- 
isms of nutrition. This concept of intelligence is well formu- 
lated in the definition of Stern (28) who says (p. 3) : "Intelli- 
gence is a general capacity of an individual consciously to ad- 
just his thinking to new requirements : it is general mental adapt- 
ability to new problems and conditions of life." In this definition 
stress is laid on intelligence as a capacity, which is general, whose 
function is to facilitate adaptation, consciously, to changed con- 
ditions. Hence memory, habit, association, learning and such 
specific mental processes are excluded from intelligence. They 
are rather as Binet has said 'phenomena of intelligence,' parts 
of the whole but never the whole itself. Intelligence in some 
degree controls memory as a mental process, and memory as a 
process conditions to some degree the amount and kind of in- 
telligence which an individual possesses, but the one is never the 
other. And so of the other phenomena of intelligence. 

Intelligence and Intellect. — It is necessary, for some purposes, to differ- 
entiate intelligence from intellect. This is a difficult matter since in com- 
mon usage the terms are interchangeable. Mark Baldwin's Dictionary of 
Philosophy and Psychology gives 'intelligence' as a synonym for 'intellect' 
and recognizes no clear distinction between the terms. He favors the use of 
either term to stand for cognitive capacity. There is, however, some in- 
clination among modern psychologists to keep a distinction between these 
terms and a tendency is observed to restrict intelligence to the capacity for 
understanding (or conscious adaptations) and intellect to the sum-total of 
the understanding (or adaptation mechanisms). Or, intelligence is con- 



4 EDGAR A. DOLL 

sidered as "the intellect as an innate capacity or endowment" (cf. Webster). 
We note a difficulty in the use of adjectives when one attempts to dis- 
tinguish between intelligence and intellect. The adjectives 'intelligent' and 
'intellectual' commonly mean 'possessed of intelligence' or 'characterized by 
evidence of intellect.' 'Intelligential' is the adjective for things pertaining 
to intelligence, but this term is not commonly used. We shall therefore 
adhere to the common usage and employ 'intellectual' as the adjectival form 
of intelligence to mean relation to intelligence. By 'intellectual growth' we 
shall hereafter mean specifically growth in intellect as a capacity. 

To sum up then, we may recognize intelligence as an aspect of 
mental operation rather clearly set apart by common consent 
from emotion and will as concomitant aspects. We may con- 
sider intelligence in four ways : ( I ) as a general ability, other- 
wise undefined, which pervades and controls all mental action out- 
side the field of emotion and will, or (2) as a compound of the 
specific mental processes of structural psychology, or (3) as a 
fundamental faculty whose essential activities are judgment, 
comprehension and reasoning and in relation to which the so- 
called simpler mental processes are phenomena, or (4) as 
a general capacity for conscious adaptation to new conditions of 
life. 

It is perhaps well to remark that the term 'intelligence' has long been 
used in the field of animal psychology with a rather different meaning. In 
animal psychology, however, 'intelligence' seems at first to have been used 
in a rather figurative sense to contrast instinctive reactions with modifiable 
or learned reactions. The degree of modifiability of response seems to 
have been taken as a measure of any living organism's intelligence. But 
when one searches for definitions or criteria of intelligence in the field of 
animal psychology one finds little clearness of meaning. Some careful 
writers avoid the term with evident purpose. Thorndike (32) gives no 
direct definition of animal intelligence but appears to identify it with the 
associative process (p. 20). Thorndike rather indirectly indicates that his 
criterion of intelligence is ability to 'profit from experience.' Holmes (20) 
defines intelligence as 'the power to form associations' (p. 181). These are 
apparently analogous if not identical with Loeb's criterion of 'associative 
memory.' 

There is reason for taking exception to the use of intelligence in these 
meanings on the grounds of etymology. From the point of view of ety- 
mology 'intelligence' must include the idea of understanding, comprehension 
or reasoning (cf. any dictionary). This cognitive element of intelligence is 
accepted as essential by Mark Baldwin. 

The course of intellectual growth. — From this hasty review of 
the concepts of intelligence now current in psychology it appears 



THE GROWTH OF INTELLIGENCE 5 

that the most acceptable definition of intelligence for purposes 
of this study is the formulation of Stern, namely, that intelligence 
is the general capacity for conscious adaptation to new situations. 
This formulation has met with practically universal approval 
among students of human intelligence (though it may not fit the 
needs of animal psychologists). Intelligence is, then, mental 
power to grasp and adequately deal with new problems. It may 
be measured ( i ) by means of a few types of problems, each type 
graded in difficulty (as in the Army Group Test Alpha and the 
scales devised by Squires and by Woolley), or (2) by means of 
a graded series of many different types of problems (as in the 
Binet Scales). 

Both methods are employed in measuring intelligence, indeed 
they have given rise to two schools in applied mental measure- 
ment. Without going into the academic question of the relative 
merits of the two methods we may say that while the method 
of many problems graded plus or minus (passed or missed) in 
a scale of approximate difficulty has proved most successful 
in individual mental examinations, the method of a few problems 
which yield a quantitative measure of success in each has recently 
proved eminently successful for group mental examinations, not- 
ably in the Army. 

By either method the practical result is much the same when 
allowance is made for statistical inaccuracies and inadequate 
standardization of test materials. To be successful such scales 
and tests must actually measure general power to apprehend 
rather than special accomplishment or specific aptitudes. Grant- 
ing such a scale, adequately standardized and of sufficient range, 
what is the course of growth that we should expect to be regis- 
tered by such a scale when applied year after year to individual 
subjects throughout their development periods? This is a prob- 
lem of immediate and pressing importance for theoretical psy- 
chology as well as for the applications of psychology to the 
problems of human welfare. 

Average normal mental growth. — The Binet Scale is stand- 
ardized empirically in such a manner that unselected subjects of 
different ages will obtain mental age scores which on the aver- 



6 EDGAR A. DOLL 

age correspond to their average life ages. The statistical meth- 
ods underlying such standardization in relation to the single 
tests in the Scale are as yet empirical. Their present sole justi- 
fication lies in the empirical satis f actor iness of the Scale. 

Otis (27) has made the most careful logical and mathematical analysis 
of the statistical principles underlying the Binet Scale and has developed an 
acceptable method of standardizing single tests in a scale of the Binet-Simon 
type. He fails, however, to apply his method to the combination of several 
tests in a year group. This is a problem not merely of determining prob- 
abilities in the single tests but of probabilities in the combined tests. Such 
combination is of course affected by the correlation between the tests com- 
bined. This is an indispensible second step which must be taken if the 
problem is to be solved in its entirety. 

Binet and Simon were satisfied to standardize their single tests on the 
criterion of a majority of 'passes' for the age at which the test was con- 
sidered standard. They failed to relate this to the number of passes at pre- 
ceding and succeeding ages, which necessity is emphasized by Otis. Binet 
and Simon also failed to calculate the percentages of combined tests passed 
at given ages. 

Most attempts to standardize the Binet Scale are based on a criterion which 
locates the individual tests of the Scale at the year where approximately 75 
per cent of subjects pass the test. Stern (28) concludes that there is no 
logical justification for using this '75 per cent of passes' as a criterion for 
locating single tests, and accepts it solely on the ground that 'it works.' 

Terman in effecting the Standard Revision cuts the knot by frankly stating 
(30, p. 54) : "We had already become convinced, for reasons too involved 
for presentation here, that no satisfactory revision of the Binet Scale was 
possible on any theoretical consideration as to the percentage of passes 
which an individual test ought to show in a given year in order to be con- 
sidered standard for that year." He decided (p. 53) that: "The guiding 
principle should be to secure an arrangement of the tests and a standard of 
scoring which would cause the median mental age of the unselected chil- 
dren of each age group to coincide with the median chronological age." 
This method of Terman obviates the difficulty of combined tests but ignores 
the problem of properly locating the single tests. Yet this problem cannot 
be ignored, and it appears from Terman's tables of standardization statistics 
(31) that he did locate the single tests according to the general principle 
employed by Binet. 

The writer has himself experimented with several methods of standardiza- 
tion (11) and has presented statistics on the percentages of subjects, both 
normal and feeble-minded, who pass various combinations of tests, thus ob- 
taining direct measures of the probabilities of passing single tests and 
various combinations. This yields not only median age distributions com- 
parable to those of Terman but also yields a measure of 'scattering' or 
range of tests passed. 



THE GROWTH OF INTELLIGENCE 7 

When experimentally standardized, by whatever criteria, the 
Binet Scale is expected to yield results such that the median men- 
tal ages will correspond to the median life ages when the subjects 
are unselected. This is, of course, an arbitrary empirical curve 
of growth in which the relative values of the mental age units 
for different parts of the scale are not known. It is based on the 
arbitrary assumption that increments in mental age from year 
to year are equal in amount, one year of mental age correspond- 
ing at all points to one year of life age up to the age-limit of 
growth. This curve of growth is of the form shown in Fig. 1. 
Its equation is y = x up to x = 13.5, where the age-limit of 
r 3-5 years is assumed as the life age when growth is complete. 



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Mental age growth curve of average normal intelligence. 
Fig. 1 



8 EDGAR A. DOLL 

It is commonly accepted that the true curve of mental growth, 
plotted in equal units of absolute mental age increments (as op- 
posed to the relative or empirical units of Fig. i ) is of the gen- 
eral form shown in Fig. 2. This is because of the general as- 
sumption that the true curve of intellectual growth is similar in 
form to the growth curves of physical development (such as 
height, weight, brain weight or nearly any physical trait). It is 
also argued by analogy with the growth curves of development 
in sensory and motor functions. 

But careful theoretical consideration of experimental and ob- 
servational child study strongly suggests a slight yet important 
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Traditional theoretical growth curve of average normal intelligence. 

Fig. 2 



THE GROWTH OF INTELLIGENCE 9 

general intelligence we mean a general capacity for adaptation to 
new situations. This adaptive capacity seems to develop very 
slowly in early infancy as is witnessed by the very small number 
of intellectual acts performed by infants. The number and di- 
versity of these acts increase very slowly in the first few years of 
life. They seem, however, to increase rapidly because each slight 
increase is a tremendous relative increase. It seems that infancy 
is a period of intellectual germination rather than growth. 
Growth itself does not go rapidly forward until early childhood, 
say about 4 years of age. Then growth proceeds rapidly, fol- 
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Life age 

Modified theoretical growth curve of average normal intelligence. 

Fig. 3 



io EDGAR A. DOLL 

which is as yet indefinitely determined but is probably not higher 
than 14 years of age. On these presumptions and assuming these 
approximate age-points we may plot a 'true' curve as in Fig. 3, 
which is a modification of the curve in Fig. 2. 

Whatever the exact form of the true curve of intellectual 
growth may be is only of passing interest for this study. For 
present purposes we must adhere to the general form of curve 
represented ideally in Fig. 1. Two principal applications of the 
Binet Scale (18, 31) to large numbers of subjects yield curves 
which approximate that shown in Fig. 1. It is interesting to 
note that one of these studies used a form of the Binet Scale 
where the single tests of the Scale were located by the cri- 
terion of 75 per cent of passes at a given age. The other ignores 
this principle and seeks directly to obtain median mental ages 
which correspond as closely as possible to the median life ages. 
Yet by either method the result is much the same within the effi- 
ciency limits of the two scales. 

In 191 1, Goddard reported his results of applying a slightly 
modified form of the Binet 191 1 Scale to 1597 school children. 
The median mental ages in relation to median life ages (ages 
taken to last birthday) as calculated from Goddard's Table 1 
(18) are shown in Fig. 4. 

It will be observed from Fig. 4 that while the Goddard Scale 
gives on the whole an empirical straight-line growth curve of the 
general equation y = x, yet the steps are slightly unequal. This 
may have been caused by errors in the location of the individual 
tests, or by selective influences governing the nature of the sub- 
jects at the several ages. That the calibration of the Scale is 
inaccurate in both the ways here suggested will be showed later. 

Terman has revised and extended the Binet Scale. This re- 
vision has been applied to 1,000 primary school children. Par- 
ticular care was exercised in obtaining standard conditions and 
unselected subjects. Terman does not present a distribution table 
showing the mental ages distributions at each life age. He gives 
instead a graphic presentation of intelligence quotients (mental 
ages divided by life ages) for each age group (ages taken to 
within two months of each year-period). Calculations of median 



THE GROWTH OF INTELLIGENCE 



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Life age 

Median mental age growth by the Goddard Binet Scale. 
Fig. 4 

1. Q.'s 2 made from these graphs (31, pp. 33 to 38) enable us to 
plot Terman's results as in Fig. 5. This yields an average 
growth curve of intelligence which is a very close approximation 
to the ideal curve of this character as shown in Fig. 1. To ob- 
tain this effect, however, was the guiding principle of the stan- 
dardization, namely, "to secure an arrangement of the tests 
which would cause the median mental age of the children of 
each age-group to coincide with the median chronological age." 

It is of interest to note that the Goddard Scale gives an em- 
pirical growth curve which is in general similar to that of the 

2 Intelligence quotients. 



12 



EDGAR A. DOLL 



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Median mental age growth by the Stanford Binet Scale 
Fig. 5 



Stanford Scale. This is in spite of the fact that the Goddard 
Scale was the first experimental study of its kind on a large 
group, and that Goddard purposely avoided all but the most 
necessary re-locations of tests in the Scale in order not to effect 
a serious revision. It is of additional interest that the Goddard 
Scale, standardized on principles of locating the individual tests, 
gives essentially the same results as the Stanford Scale, which 
disregards this principle and deliberately adjusts the Scale until 
it has forced the median mental ages to correspond to the median 
life ages. 

It will be noted that the curves presented in Figures 4 and 5 



THE GROWTH OF INTELLIGENCE 13 

reach final levels. In Fig. 4 the level is reached at 10 years of 
life age. This is because by the Goddard Scale it was not pos- 
sible to obtain a mental age score greater than 13. Indeed, a 
mental age score of 13 by this Scale was unusual because of cer- 
tain imperfections in the tests that one could pass above the level 
of 12 years. Hence the upper range of possible deviations in 
intelligence after about 10 years cannot register themselves by 
the Goddard Scale. It has, however, long since been pointed 
out that the Goddard Scale is not a valid measure after 10 years 
of mental age (12). 

Similarly, by the Stanford Scale the final level of intelligence 
is reached at 14 years of age. Terman, however, believes that 
his 15-year and 16-year subjects were of sub-average intelligence, 
because they were over-age for the 7th and 8th grades. He fur- 
ther believes that the true average level is about 16 years, this 
being the median mental age of 32 high school students and 60 
business men. In accounting for this 16-year level Otis (27, 
p. 137) asserts as a fact that, "the number of 17-year-olds, 18- 
year-olds and 19-year-olds who exceed 16-year intelligence is 
practically the same as the number of 16-year-olds who exceed 
it" and that "this suggests that while intelligence increases with 
age, the increments decrease with age, and that after about the 
age of 16 years the intelligence does not increase at all, or but 
very little." Terman says (30, p. 140) ; "Native intelligence, in 
so far as it can be measured by tests now available, appears to 
improve but little after the age of 15 or 16 years. Although 
the location of this point is not exactly known, it will be suffi- 
ciently accurate for our purpose to assume its location at 16 
years." 

In opposition to these views we venture the same explanation 
of the assumed 16-year level by the Stanford Scale that we have 
just offered (and is commonly accepted) as the explanation for 
the 10-year level by the Goddard Scale. That is to say, the range 
of tests above the 16-year level in the Stanford Scale is so narrow 
and their nature so questionable that individual differences are 
not brought into display after this level. Hence, the 16-year level 
is the 'efficiency limit' of the Stanford Scale. There is reason 



i 4 EDGAR A. DOLL 

to believe that the true age of average arrest of mental age 
growth is actually between 13 and 14 years as indicated in Fig. 5. 

Results from the psychological examining in the army and other data 
(cf. 6) suggest that the level of the true average adult is midway between 
the 10-year level of the Goddard Scale and the 16-year level of the Stanford 
Scale. 

It is evident that Terman's 62 adult subjects (31) were selected in favor 
of superior intelligence on the basis of education or occupation. An average 
adult group to be unselected must include the gamut of occupations from 
unskilled labor to high professional skill, and the gamut of education from 
illiteracy to college education. These groups must be weighted according to 
the frequencies in each class. But Terman's adult subjects whose median 
mental age was 16 years were 30 successful business men and 32 high school 
students. Both groups are of superior selection, the one by occupation and 
the other by education. Terman's grammar school groups whose ages were 
15 and 16 years did not exceed the median mental age of 14 years. The 
fact that they were over-age for this grade does not mean they were of 
sub-average intelligence unless they were also below the 7th school grade. 
Statistics of school retardation indicate that less than 50 per cent of all 
pupils who enter school pass beyond the 7th grade. Hence those who do go 
beyond the 7th grade are the supra-average individuals. If 7th grade school- 
ing corresponds to 13-year intelligence, and if the average individual does 
not pass beyond the 7th grade, then the average individual has 13-year in- 
telligence (assuming perfect correlation and equal educational opportunity). 

Or we may obtain the true median mental ages for 15 years and 16 years 
by combining the medians of those subjects of these ages who are in high 
school with those who are in the grammar school. This would yield median 
mental ages of about 14 years for these age-groups. 

In a later work Terman presents the results of several studies of the re- 
lation of intelligence to occupation (29, pp. 268-290). Median mental ages 
are given as follows (p. 286) : college students 17.4 years, business men ("of 
moderate success and limited educational advantages") 16.3 years, express 
employees 15.2 years, motormen and conductors 13.8 years, firemen and po- 
licemen 13.4 years, salesgirls 13.6 years, hoboes and unemployed 14.2 years. 
The median intelligence of common laborers and unskilled workers is pre- 
sumably under 13 years. Hence a representative or totally unselected or 
random sampling group of adults weighted according to the occupational 
distribution of the country at large (with larger numbers in the lower 
classes) would give a median mental age or average adult level of intelli- 
gence presumably not higher than about 13 years. This is exactly what 
was found from psychological measurement and investigation in the army, 
where the median mental ages of nearly 1,500,000 unselected recruits was 
found to be about 13 years (cf. 6). 

We may conclude, then, that the average normal curve of in- 
tellectual growth obtained by the Binet Scale is a straight line 



THE GROWTH OF INTELLIGENCE 15 

of the equation y = x. By the Goddard Scale this equation is 
approximately satisfied up to the point where x = 10, that is 
up to a mental age of 10 years. By the Stanford Scale the equa- 
tion is satisfied with somewhat closer approximation up to the 
point where x = 16. But the average adult level of intelligence 
is only between 13 and 14 years according to the best available 
evidence. This latter conclusion challenges the validity of the 
standardization of the Stanford Scale beyond the age of 14 years 
in terms of the intelligence of the average individual. For if 
it is a fact that the intelligence of the average normal individual 
reaches a final level at 13 or 14 years of age, then the average 
intelligence of unselected subjects at 15, 16, 17, 18 and 19 years 
must be the same as that 13 or 14 years. Hence the standardiz- 
ing of tests by year-intervals after ages 13 or 14 must be ac- 
complished by some statistical device other than that employed 
for the Stanford Scale. 

Subnormal growth of intelligence. — The growth curves of in- 
telligence for subnormals are dependent upon the specific rate of 
growth and the specific age of final arrest which characterize the 
specific type and degree of subnormality. For normal subjects 
the rate of growth is on the average constant at 1.00. This is 
a necessary consequence of the empirical nature of the Binet 
Scale which we have seen is so devised as to yield median mental 
ages which are equal to the median life ages of the subjects on 
whom the scale is standardized. And for normal subjects the 
age of final arrest is that age at which the curves of distribution 
for superior ages coincide. This age may be 15 or 16 or higher, 
but for reasons given may be placed provisionally at 13 years. 

Age of arrest for subnormals. — In a previous publication (6) 
the hypothesis was developed that the age of final arrest is ap- 
proximately identical, on the average, for widely different mental 
and social types, and is so independently of the level of final 
arrest. This age of arrest was found to coincide with the level 
of arrest of the average adult, which was provisionally placed 
at 13 years. 

We shall now on theoretical grounds take certain exceptions 
to this hypothesis that the age of arrest is independent of the 



16 EDGAR A. DOLL 

level of arrest and later question both theory and hypothesis by 
the experimental data of this study. Our theory is most clearly 
expounded by a consideration of the extremes of intelligence 
deviations. 

Experience with institutional feeble-minded strongly suggests 
that for this type of subnormal intelligence the age of intellectual 
arrest is a function of the final degree of subnormality. Obser- 
vation leads one to believe that idiots are arrested in their in- 
tellectual growth very early in life (say at about the life age of 
5 or 6 years), that imbeciles are arrested at a somewhat later 
age (say about 10 or 12 years), and that morons are arrested 
still later (say about 15 years). 

Several years ago Goddard concluded that the feeble-minded, 
in the majority of cases, were at a stage of arrest when they had 
become four years retarded mentally, that is when mental age 
was four years behind life age (17). He found only 6 per cent 
of 252 feeble-minded subjects (defined by him as those who are 
4 years retarded) gaining more than 1.0 year after three annual 
examinations (a two-year period). These were all 'younger 
cases' and some 'receiving special treatment.' 

Binet and Simon raised the question early in their work. 
After mentioning the lack of knowledge, the need for experi- 
ment and the difficulty of obtaining data, they say (2, p. 143) ; 
"No doubt it is possible — perhaps even probable — that a child 
who at five years has scarcely the intellectual level of a child of 
two, will be the same at ten or fifteen years. Without doubt one 
can suppose that the cerebral defects which have thus far pre- 
vented the acquisition of ordinary ideas, would remain a definite 
obstacle. But we have no right, without the facts, to affirm this." 

Likewise Stern says (28, p. 84) : "The feeble-minded child 
. . . reaches a stage of arrest at an age when the normal child's 
intelligence is still pushing forward in its development." 

Terman (29), on the other hand, maintains that mental growth 
develops at a constant rate for all degrees of brightness and dull- 
ness (except idiots and low-grade feeble-minded) and makes no 
reservations regarding the age of arrest for the feeble-minded. 
He calculates the relative intelligence of feeble-minded subjects 
on the same age-limits as for normal subjects. 



THE GROWTH OF INTELLIGENCE 17 

Kuhlman (22) also after long experience with the institutional 
feebleminded assumed that all types of feeble-mindedness (ex- 
cept perhaps idiots) reach their level of final arrest at 15 years 
of age, without regard to the several degrees of defect. 

The writer has previously speculated on the same subject (9) 
at which time he suggested that the age of arrest was reached 
when the mental age retardation amounted to either 6 years or 
was 50 per cent below life age. In conclusion it may be said 
that the question has never been decided on the basis of sufficient 
evidence. 

The rate of growth for subnormals. — Not much more is known 
about the rate of mental growth among extreme subnormals, like 
the feebleminded, than about the age of arrest. In this regard 
we are even at a loss for adequate observational data. Experi- 
ence with institutional feeble-minded, however, suggests a great 
variety of possible forms of retardation curves. Such experience 
points to a small but significant group of feeble-minded who 
grade 'at age' by the Binet Scale when first examined but who 
make no material progress in later examinations over a period of 
years (Type A, Fig. 6). There are others (Type B, Fig. 6) 
who at the time of first examination test at age, then continue to 
develop at a retarded rate for a time and then reach a point of 
arrest. There is a third group (Type C, Fig. 6), already re- 
tarded when first observed, who from the first examination to 
the age of final arrest develop at an annual rate of growth which 
is a constantly decreasing variable. There is also a fourth group 
(Type D, Fig. 6) who from the time of first examination to the 
age of final arrest develop at a constant rate up to the age of 
arrest. There are many variants and combinations of these 
basic types for individual subjects. We believe, however, that 
these four types comprise the majority of the feeble-minded. 
It is conceivable, though not probable, that some individuals might 
have a higher than average rate before retarding. It is also con- 
ceivable, though not likely, that the arrest might be relatively 
greater in the early ages with a curve of growth which would be 
accelerating at some intervals. It remains for experimental in- 
vestigation to show the relative frequencies of these different 



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EDGAR A. DOLL 



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Theoretical growth curves of individual feeble-minded subjects. 

Fig. 6 

types of growth curves. Our own data contribute to this end, 
in consequence of which we shall be able to plot a number of in- 
dividual growth curves of feeble-minded subjects covering a 
fairly long period of years (cf. Figures 12 to 15, pp. 107 to 118). 

It is interesting to compare these observations with the opinions of other 
writers. 

Binet and Simon anticipated this problem as they did so many others aris- 
ing from the use of their Scale. They say (2, p. 143) : "It is necessary to 
follow individually very many subjects in their development, to see if the 
states of intellectual inferiority are caused by arrested development, or by 
very slow evolution continued irregularly or intermittently, or to see if some 
essential faculties could increase while others remained stationary or un- 
developed." There is a suggestion in their work not only of the contrast 



THE GROWTH OF INTELLIGENCE 19 

between suddenly arrested development (our Type A, Fig. 6) and gradu- 
ally increasing retardation (our Type C, Fig. 6), but also the hint that there 
may be some relation between the character of growth curve and the etiology 
of the subnormality. They were also of the opinion at that time (1905) 
that the course of growth was not predictable. 

Goddard raised the question again in 1913. He says (15, p. 125) : "How 
does the child reach his point of arrested development? Is it by a gradual 
slowing down or by a sudden stop? . . . Perhaps it is a matter of the in- 
dividual. Some develop one way and some another. . . . There are some 
indications, however, that some children are pretty nearly normal until about 
eight or nine or ten years of age, and then they stop rather suddenly. . . . 
Others seem to have always been a little backward, but keep getting more 
and more backward until the age perhaps of nine or ten, when they seem 
to have entirely stopped." 

In a later work (16, p. 61) Goddard says: "Experience has proved that 
these cases have a slowing down period of probably from one to three years. 
Moreover the slowing down process may begin at any time during child- 
hood. Of course, with the idiot the matter is relatively quickly settled; 
with the imbecile less quickly and with the moron it becomes a problem for 
a number of years. ... It does not appear likely that all such defectives 
have the same rate of slowing down; some probably reach the stopping 
point more quickly than others, just as some begin the slowing down process 
at an earlier age than others." Individual growth curves are presented in 
support of the argument. 

Stern, generalizing from Binet, states the following thesis (28, p. 72) : 
"For every feeble-minded child there is a level which, once attained, repre- 
sents a definite terminus for his capacities to meet the demands of mental 
tests." He then examines this thesis in an endeavor to discover when the 
terminus is reached and how (that is, by what course) it is reached. He 
sharply distinguishes arrest from retardation, the criterion of the former 
being the arrival at the terminus and the criterion of the latter being the 
process of reaching the terminus. Concerning the rate of growth he says 
(P- 79) : "Since feeble-mindedness consists essentially in a condition of de- 
velopment that is below the normal, the rate of development will also be 
a slower one." From these premises Stern develops the 'intelligence quo- 
tient' as a means of measuring relative retardation and rate of growth. He 
says in regard to this quotient (p. 83) : "The quotient does not seem, how- 
ever, to afford an actually constant expression of degree of feeble-minded- 
ness, but shows a tendency to fall in value as age increases." And further: 
"The above-mentioned gradual tendency of the mental quotient to sink during 
the progress of development shows that this development approaches the 
final level of arrest at a progressively decreasing rate." 

Bobertag is credited by Stern as "laying special emphasis on this progres- 
sive rate of retardation in the development of the feeble-minded" and as at- 
tempting to express it graphically. (We shall subsequently present a de- 
tailed analysis of Bobertag's position.) 

Kuhlmann (22) conceived the idea of an intelligence quotient about the 



20 EDGAR A. DOLL 

same time as Bobertag and Stern. His material led him to the assumption 
that the rate of feeble-minded growth is constant throughout the develop- 
mental period and up to 15 years of age for any given degree of feeble- 
mindedness except idiocy. But he recognizes that this assumption holds only 
for the averages and might be found invalid for individual cases. He cites 
the possibility of an increasingly retarded rate in particular subjects. 

There is a growing body of literature which deals with the rate of de- 
velopment from the standpoint of intelligence quotients. In a succession of 
important studies since 1915, Terman has consistently argued that intelli- 
gence quotients tend to remain constant. This point of view is critically 
analyzed in a later section. 

The writer has himself previously contended that the rate of develop- 
ment among individual feeble-minded subjects is exceedingly variable and 
non-predictable (9). The fact that some feeble-minded develop at a normal 
rate early in life and then rapidly slow down in development (at about eight 
or ten years of age) has led the writer to recognize a condition of 'potential 
feeble-mindedness' (8, 10), a clinical type of feeble-imindedness in which in- 
telligence retardation is not observable at the time of diagnosis, yet where 
the diagnosis is upheld by the subsequent history of the individual. 

From this review of the field we find some difference of opin- 
ion. It may be well to suspend judgment for the present. The 
experimental evidence of the present investigation is intended to 
throw light on this problem, which is of fundamental interest in 
mental diagnosis. 

Logical considerations lead to the belief that the age of arrest 
and the rate of retardation are both functions of the level of ar- 
rest, on the average at least. Psychological and logical consid- 
erations indicate that for the feeble-minded it is probable that 
the rate of growth is a decreasing variable. This will not pre- 
vent us from admitting, however, the possibility of many kinds 
and degrees of individual variation. Theoretical curves based on 
these logical and psychological considerations are given in Fig. 7. 

Supernormal growth of intelligence. — We may now apply the 
same general argument as developed above to the question of 
growth curves of supernormal deviations in general intelligence. 
On a priori grounds it would seem that persons of superior in- 
telligence tend to become increasingly superior, that is, they tend 
to develop at a rate of growth which is an increasing variable. 
If (1) the intellectually subnormal develop at a regularly de- 
creasing rate; and if (2) the average unselected rate based on a 



THE GROWTH OF INTELLIGENCE 



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composite of subnormal, average normal and supernormal is 
constant at all ages; and if (3) there are as many supernormals 
as subnormals ; then it is highly probable that the decreasing rate 
of the subnormals must be offset by an increasing rate for the 
supernormals. Otherwise the decreasing rate of the subnormals 
would in some degree affect the constancy of the total average 
rate for all unselected subjects. The only other possibility is 
that the decreasing rate of the subnormals is offset by an increase 
in the number of supernormals rather than in the rate for super- 
normals. This is a tenable hypothesis, for if some subjects of 
'at age' intelligence are potentially feeble-minded it is certainly 



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also likely that others are potentially gifted. But since the per- 
centage of average normals must remain constant (being by 
definition the middle 50 per cent of all cases) it is more likely 



THE GROWTH OF INTELLIGENCE 23 

that the decrease in rate of subnormals is actually compensated 
for by an increase in the rate of supernormals. 

There is, however, very little basis of fact on which to base 
speculations regarding the rate of growth of gifted children. 
Very few experiments have been made on a large scale. We need 
long-time studies of individual re-examinations. Terman, how- 
ever, comes to the conclusion that the rates of development of 
superior children are constant just as he finds they are constant 
for average normals and subnormals. Miss Gillingham, how- 
ever, one of the few other students who has made re-examina- 
tions of superior children, finds her subjects quite variable, some 
increasing and some decreasing. We shall examine these points 
of view more carefully in a critique of intelligence quotients and 
by some new experimental evidence. For the present we may 
content ourselves with two probable hypotheses, (1) that the 
rate of growth of superior children is an increasing variable, the 
growth curve following the general form of Type A, Fig. 8, or 
(2) that the rate is constant throughout the development period, 
the growth curve being of the general form of Type B, Fig. 8. 



II. EXPERIMENTAL INVESTIGATION 

Having defined our terminology, stated our point of view and 
advanced certain theoretically developed hypotheses, we may now 
pass to the justification of these hypotheses in the light of experi- 
mental evidence. Our major experimental study is based on ten 
years of re-examining feeble-minded subjects of all ages, mental 
ages and degrees of relative retardation. Our minor experi- 
mental study is based on three years of re-examinations of su- 
perior children between the ages of 9 and 13 with I. Q.'s of at 
least no at one or more of the examinations. 

A. Feeble-Minded Growth 

History of the experimental data. — The Binet-Simon tests 
were introduced into this country about 1908- 1909. At that time, 
Dr. Henry H. Goddard, Director of Research at The Training 
School at Vineland, N. J., employed the 1905 series of tests as a 
means of classifying the feeble-minded 'children' at the Training 
School. In 191 o, the 1905 series of tests was replaced by the 
Binet-Simon 1908 Scale (13) which was applied systematically 
to all inmates of the Training School. The results were so re- 
markably superior to those which had been previously obtained 
by the limited technique of mental tests then in use and were 
found to correspond so closely with all other experience with 
these feeble-minded that the 1908 Binet Scale was made the basis 
of classification and grading at the Training School (cf. 14). 

Goddard immediately foresaw the great value of the Binet 
Scale as a means of measuring the mental 'unprovability' or in- 
tellectual growth of the feeble-minded. He accordingly provided 
for annual re-examinations of his subjects. At the same time 
he proceeded to correct certain inaccuracies in the method by 
standardizing the 1908 Scale on a large body of American school 
children (cf. 18). This standardization of the Scale proved to 
be sufficiently accurate for all practical purposes and became the 
fundamental psychological method in use at The Training School 



THE GROWTH OF INTELLIGENCE 25 

from 191 1 to 1916. This form of the Binet Scale was continued 
as the examining method for measuring growth of intelligence 
for the subjects of this experimental study until Dec. 1919. 

The data of this experimental investigation are based on the 
results obtained in 19 10 by Goddard's translation of the Binet- 
Simon 1908 Scale, and between 191 1 and 1919, inclusive, by the 
so-called Vineland Revision, or Goddard Revision of the Binet 
Scale (13). 

There is some objection to including the 1910 test-records in 
this investigation. There is sufficient difference between the 
two scales used to warrant an objection to the validity of com- 
paring the resultant mental ages. Nevertheless it is desirable to 
retain these very early records for the sake of the long time- 
interval they afford between first and last test-records. More- 
over, the discrepancy between the two scales is not, after all, of 
much practical consequence, since the mental ages by the two 
different scales are closely similar. 

In order to preserve these early records and yet maintain uni- 
formity of material all 1910 records have been transcribed in 
terms of the Goddard (1911) revision. This transcription of 
course affects many of the single tests of the 1910 examinations, 
since some of the tests of the 1908 Goddard Scale are excluded 
from the 191 1 Goddard Scale. Other tests may not properly be 
transcribed from one Scale into terms of the other because of 
modification of procedures either in administering or scoring the 
individual test. All such tests, namely those of the 1908 scale 
which do not appear in the 191 1 scale at all or else appear in 
modified form, have been excluded from the final data. 

These transcribed records were in consequence of these diffi- 
culties sometimes incomplete. If the incompleteness was so 
great that it could not safely be made good by means of certain 
rules (to be discussed presently) for scoring incomplete tests, then 
the entire test-record for that year was discarded. If, however, 
the incompleteness could be provided for under those objective 
rules for scoring incomplete records, then the scores for the omit- 
ted single tests have been supplied under those rules, as will be ex- 
plained. 



26 EDGAR A. DOLL 

An additional and more serious factor leading to the incom- 
pleteness of 1910 records is found in the narrow-range method 
of testing employed during those years. This also has been 
overcome by the use of objective rules for scoring incomplete 
examinations. 

The data have been collected by a large number of different 
examiners. The examinations during 1910, 191 1 and 1912 were 
made principally by Dr. Goddard's assistants carefully trained in 
the method. During these years an attempt was made to examine 
the entire number of children residing at The Training School. 
The results of these repeated examinations were reported by 
Dr. Goddard (15, 17) in 1912 and 1913. 

Goddard appreciated the preliminary nature of his investiga- 
tion and recognized the need for study covering a longer period 
of time. It is to his good judgment and foresight in this regard 
that we owe the collection of data upon which this present report 
is based. The personal direction and analysis of these continued 
examinations was, in 191 3, assigned to the present writer as his 
major routine duty as assistant to Dr. Goddard. Accordingly 
the collection of data for the present study was entirely in the 
hands of the writer after 191 2, except for such examinations as 
were conducted during the annual Summer Schools held at The 
Training School. These latter examinations were conducted 
under the immediate supervision of Dr. Goddard, Dr. F. Mateer, 
Dr. S. C. Kohs and Dr. C. T. Jones during successive summer 
periods. 

After 191 2 an attempt was made to regulate the time-interval 
between re-examinations by establishing a calendar file of rec- 
ords. Provision was made for re-examining new cases one 
month after admission to The Training School and for re-exam- 
ining twice a year all children under 15 years of age. All ex- 
aminers were carefully trained in the method before their results 
were admitted to record. Apparatus, technique and standards of 
scoring were minutely standardized. Wide-range testing was 
demanded in all records. The work of unskilled examiners was 
closely supervised. Summer school records were labelled as such 
and unless approved by the supervising instructor were not ad- 



THE GROWTH OF INTELLIGENCE 27 

mitted to the data of this investigation. In all examining it 
was considered a prime duty of the examiner to secure a favor- 
able attitude. 

From this it will appear that the data are somewhat subject to minor in- 
accuracies on the ground of examiners' personal equation. Goddard has 
reported an influence of personal equation (17), but is of the opinion that 
personal equation is of little significance among mental defectives who are 
retarded four years or more. Brigham also (5) has studied personal equa- 
tion with minute accuracy, and is of the opinion that while personal equa- 
tion is evident on single tests in the Scale it is imperceptible in the total 
mental ages. This imperceptibility is presumably due to compensating in- 
fluences in the single tests, variability operating in favor of the subject on 
some tests and against him on others. In general it may be said that per- 
sonal equation is a complex of variations in apparatus, technique of admin- 
istration and of scoring, personality or attitude of subject and examiner 
and consequent rapport, and various internal and external additional factors 
influencing both examiner and subject in varying degrees at different times, 
such as time of day, pleasantness or unpleasantness of atmosphere or physi- 
cal surroundings, presence of observers, physical well-being, need for haste, 
pre-judgment of the subject's mentality, skill in 'handling' the subject or in 
manipulating the method, and so forth ad finem. Most of these influences 
are not subject to measurement and among mental defectives are either 
negligible or tend to offset each other. 

Special objections might also be raised against the use of Summer School 
data on the ground of specific inaccuracy. In answer to this objection we 
may refer to the experimental studies of Kohs (21) and Martin (24) which 
demonstrated that for at least the School where these data were gathered 
the mental ages obtained by Summer School students after six weeks of 
intensive training and supervised examining are safely comparable with 
those obtained by highly skilled examiners. 

Description of data. — The inmate population of The Training 
School approximates 500. There is an annual change in popula- 
tion amounting to perhaps 100 new admissions to offset dismis- 
sals, releases, transfers and deaths. From 1910 to 191 7 approx- 
imately 1,000 patients have been examined and re-examined. No 
new cases were examined for the purposes of this study since 
1 91 6. This group of about 1,000 is cut to about 400 when we 
eliminate those subjects who were not examined at least two or 
three times. 

About 1913 the writer instituted a procedure of transferring 
the records of examinations from the Binet record sheets to 
summary cards. These cards were designed to show the plus and 



28 



EDGAR A. DOLL 



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THE GROWTH OF INTELLIGENCE 29 

minus responses to the individual tests on repeated examinations. 
A specimen card is shown in figure 9. This card shows the name 
of the subject, the date of his birth, and the date of his admis- 
sion to The Training School. The successive columns from left 
to right show the name of the examiner, the date of examina- 
tion, the 'basal year' and additional number of tests passed in 
the examination, the mental age, the life age, the intelligence quo- 
tient, the amount of retardation, and then the succession of 
reactions in the Goddard arrangement of the Binet tests. 

All data transcribed from original record sheets to these cards 
were carefully checked up. Wherever the original record con- 
tained material which afforded a basis for verifying the score 
assigned (plus or minus) such verification was made. This 
checking was particularly important in early test-records (prior 
to 1 91 3) since the standards of scoring did not become well sta- 
bilized until toward the close of 191 2. No scores were changed 
without evidence which permitted such changes. Records ob- 
tained by means of the 1910 Goddard version of the Scale were 
transcribed in terms of Goddard's 191 1 version as previously 
described, especial care being taken in relation to modifications 
in technique or scoring of the individual tests. 

After this card file was begun it was used as a calendar file 
to standardize the time-interval between tests. New data were 
transcribed to the cards as soon as new examinations were made. 
At various times the writer attempted to analyze the results. 
Each such attempt proved abortive owing to the exceedingly diffi- 
cult nature of the material in relation to an adequate mode of 
presentation. The material was so heterogeneous that no satis- 
factory classifications of data could be devised to represent the 
facts clearly and simply. Moreover each attempted analysis 
showed an imperative need for additional material and a longer 
period of time. Many minor problems suggested themselves as 
necessary preliminaries to the final adequate analysis. The re- 
sults of those minor studies have been previously published and 
afford support to certain arguments to be presented. 

The repeated examinations of about 400 subjects formed the 
starting point of the present report. A close study of the ma- 



3 o EDGAR A. DOLL 

terial showed the necessity for eliminating the records of certain 
subjects. It was decided to use no records which showed a gap 
of more than two years between any two successive examina- 
tions. It became obvious that records based on less than 5 an- 
nual examinations would not contribute much to the final con- 
clusions; hence all such records were excluded. Certain special 
records were also rejected on the basis of special physical in- 
firmities, such as deafness or partial deafness, seriously defective 
vision, motor ataxia, paralysis and the like. These rejections 
were made in ignorance of the significance of the data rejected, 3 
and indeed of the data as a whole, since we were not at the time 
aware of what the results might show. Three special cases were 
excluded from the final tabulations, one who was 2 years old at 
the first examination, one whose initial mental age was 1 1 years, 
and one whose final mental age was 1 1 years. These were elimi • 
nated because they fell outside the age and mental age classifi- 
cation limits of the material as a whole; all other subjects were 
at least 6 years old at first examinations and were below mental 
age 11 years. 

There remained 203 subjects. Fifty-five of these were ex- 
amined at least once every year for at least 5 years ; 72 were ex- 
amined at least once every year but one for a period of at least 
5 years ; 37 showed a single gap of two years between successive 
examinations; 17 showed 2 gaps of single years; 18 showed 1 
gap of 2 years and 1 gap of 1 year; 4 showed 3 gaps of single 
years. Ordinarily the total number of examinations per subject 
exceeded the total number of years covered by the examinations. 
On the average, for all subjects there was only slightly more 
than one examination per year. The distribution of examina- 
tions for all subjects is given in Table 1. This table shows the 
number and extent of gaps between examinations, the corre- 
sponding numbers of cases, the total number of examinations 
and the periods of time covered per subject. It will be seen that 

3 No mental ages were entered on the summary cards until after these 
subjects had been eliminated. The mental ages were not computed until 
after the individual examination records had been corrected for the errors 
of incomplete examining. To avoid bias we remained in ignorance of the 
exact mental ages until the material was ready for the final computations. 



THE GROWTH OF INTELLIGENCE 31 

the total number of subjects is 203, and the total number of ex- 
aminations 1797, giving an average of approximately 9 exami- 
nations per subject. The total number of subject-years (obtained 
by taking the weighted totals for the column headed 'period of 
years') is 1477, giving an average of approximately 7 years per 
subject. Dividing the total number of examinations by the total 
number of subject-years gives an average of 1.2 examinations 
per subject per year. 

Table i 

Description of feeble-minded data showing temporal 

distribution of examinations 

No. of No. Period of years covered 

Continuity of examinations subjects exams. 5 6 7 8 9 10 
No gap between examinations.. 55 578 21 8 8 10 4 4 

1 gap of 1 year 72 684 7 18 18 11 10 8 

1 gap of 2 years 37 260 1 1 23 7 4 1 

2 gaps of 1 year each 17 131 1 772 

1 gap of I year and 1 of 2 years 18 119 2952 

3 gaps of 1 year each..' 4 25 22 

Totals 203 1797 30 27 60 44 27 15 

Correction of incomplete examinations. — Prior to 191 3 the 
need for 'wide range' testing was not commonly recognized by 
those who applied the Binet-Simon Scale. Indeed the original 
mode of calculating mental age as advocated by Binet encouraged 
narrow range testing in the lower reaches of the Scale. More- 
over, it has always been difficult to induce even skilled examiners 
to employ wide range testing. Consequently the comparison of 
some successive examinations is affected by differences in the ex- 
tent or range of the Scale that was used in examining the sub- 
jects. In comparing repeated examinations an apparently sig- 
nificant gain in mental age may be only the result of a more ex- 
tended examination in the upper range of the Scale, or an ap- 
parent loss may be really only a consequence of a more extended 
lower range of application. A mental age obtained by narrow 
range examining is ordinarily sufficiently accurate for practical 
purposes, but it may be significantly inaccurate when compared 
with preceding or succeeding examinations in an endeavor to 
discover small amounts of mental gains or losses. 

This error in the original examinations threatened to limit the 
value of the study, for it was to be expected that the amounts of 



32 EDGAR A. DOLL 

mental age increase among the feeble-minded would prove to be 
relatively small. This fact made it imperative that the incomplete 
examination records be somehow rendered complete or that such 
records be eliminated from the data. The latter procedure 
would have eliminated much otherwise valuable material. More- 
over, the error looms larger on theoretical considerations than 
its practical significance warrants. Hence it seemed desirable to 
correct the initial data by completing the incomplete examina- 
tion records. This proved a peculiarly difficult yet not impossible 
task. 

Objective rules for completing incomplete examinations. — One 
who is well versed in the Binet method, who knows the errors of 
standardization which produce improper locations of the single 
tests, knows the comparative difficulty of the tests for feeble- 
minded, knows the influences of experience and which tests are 
affected by practice, schooling and maturity, knows the exami- 
ners and their personal equations, and knows well the subjects 
and their personal idiosyncracies will not have much difficulty in 
correcting or completing inaccurate or incomplete Binet records 
of feeble-minded subjects. He will, however, always be obliged 
to resort to considerations which are principally subjective. He 
must consider such a variety of combined considerations that he 
is liable to give unstable judgments. He would also find such a 
task exceedingly fatiguing if he endeavored to complete any 
serious number of examinations; the conflict of evidence, the 
weighting of evidence and the multiplicity of factors involved 
demand a high pitch of concentration for successful application. 
But above all his judgments could readily be challenged by soms 
other person of equal expertness and he would be unable to sub- 
stantiate his judgments in a manner that would probably be con- 
vincing to a skeptic. 

It was therefore a first task to devise an objective means of 
completing the original examination records. No attempt was 
made to correct suspected errors in scoring or recording. 

The demands of the problem, then, require an objective tech- 
nique for scoring those tests of the Scale which have not been 



THE GROWTH OF INTELLIGENCE 33 

scored on some examinations but have been scored in others. 4 
Since there is no demand to correct a test already scored, the 
rules apply only to unscored single tests. The purpose of the 
rules is not to decide the absolute probable score of a test as it 
affects the mental age of a particular examination, but is designed 
to determine the comparative probable score of a test which is 
sometimes not scored in a succession of examinations. The aim 
is to obtain a succession of mental ages which are satisfactory 
for comparative purposes and to eliminate errors which affect 
the comparisons. There is no concern as to the probable score 
of a test which does not influence the comparative mental ages. 
Hence we are not concerned about those tests which are never 
scored in successive examinations but only those which are some- 
times though not always scored. 

For these purposes the scale of tests shall be understood to 
cover three 'ranges' for each subject. These are: 

( 1 ) . A lower range, which includes in each separate examina- 
tion the series of tests from the lowest mental year of the Scale 
to the highest year (inclusive) in which all five tests for a year 
are scored plus. 

(2). An upper range, which includes the series of tests (in 
ascending order of difficulty) beyond the first year in which less 
than three tests are scored plus. 

(3). A middle range, which is the series of tests between the 
upper limit of the lower range and the lower limit of the upper 
range. 

If in any of these ranges a test of the Scale is sometimes scored 
and sometimes not scored, then a probable score for such un- 
scored tests is to be assigned in accordance with the following 
rules. The rules are to be applied in order of numerical se- 
quence ; a later rule is not to be applied if an earlier rule can be 
made to apply satisfactorily. 

Rule 1. An examination record is to be excluded entirely as 
too incomplete for accurate uses if less than 5 tests are recorded 
beyond the highest year where all tests are recorded as plus. 

4 In this discussion "test" is used to designate a single test-problem of the 
Scale, while "examination" refers to an application of the Scale as a whole 
to obtain a mental age. 



34 EDGAR A. DOLL 

Rule 2. Year IV in the Goddard Scale has only four tests 
while every other year (above year II) has five. Each test at 
year IV has therefore a value of .25 instead of .20 as at other 
years. In calculating mental ages the loss of this test at year 
IV sometimes affects the total comparative mental age, due to 
a shift in the basal year. To avoid this error and at the same 
time provide for the slightly higher value of the IV-year tests 
proceed as follows : 

(a). If three or four tests are scored plus in year IV, credit 
an extra test plus. 

(b). If only two tests are scored plus, credit an extra test plus 
and minus (half credit, or .1 year). 

(c). If less than two tests are scored plus, credit an extra test 
minus. 

Rule 3. In the following pairs of tests (Goddard Scale) one 
test-problem serves for both tests of a pair and one test-reaction 
on the part of the subject furnishes the score for both test-loca- 
tions, being automatically plus for the first of the pair if plus 
for the second, and minus for the second if minus for the first 
(plus score in the second of each pair requiring a higher type 
of response than for the first). 

III 4 (enumeration in pictures) — VII 2 (action in pictures) 
V 4 (count 4) — VIIi (count 13) 

VI 2 (define by use)' — IX 2 (define better than use) 
X 5 (3 words in simple sentence) — XI 2 (3 words in complex 
sentence). 
Therefore : 

(a). If the first is scored minus, the second must be scored 
minus ; and if the second is scored plus the first must be scored 
plus (since failure on the first includes failure on the second and 
success on the second includes success on the first). 

(b). If the first is scored plus, the second if unscored is pre- 
sumed to be minus (since otherwise the examiner must have 
recorded plus for the higher form of response) ; and if the second 
is scored minus, the first if unscored is presumed to be plus (since 
if it had been minus the examiner must have recorded it). This 
rule is based on the known tendency of examiners to fail to 



THE GROWTH OF INTELLIGENCE 35 

record plus scores in the lower range and minus scores in the 
upper range since such scores do not affect the calculation of 
mental age. 

(c). If (through an obvious error of record) both tests in a 
pair are scored in such a way as to conflict with part (a) of this 
rule, the prevailing score of the test in successive examinations 
may be appealed to for correcting the obvious error. 

Rule 4. In the following pairs of tests there is primarily a 
quantitative difference in the two test-problems; success in the 
first of the pair is generally prerequisite for success in the sec- 
ond (because the second also includes the specific test-problem 
of the first) : 

Ii (visual regard) 5 — I 3 (visually stimulated prehension) 

Ii — all tests beyond I 3 . 

I 3 (prehension visually stimulated) — Hi (visual discrimina- 
tion of food) 

I 3 (prehension visually stimulated) — II 2 (unwrapping 
candy). 

IIIi (point to parts of body) — VI 4 (designate right and 
left). 

111 2 (repeat 6-syllable sentence) — V 3 (repeat 10-syllable 
sentence) 

1113 (repeat 2 digits) . — IV 3 (repeat 3 digits) 
IV 3 (repeat 3 digits) — VIII 5 (repeat 5 digits) 

V 2 (copy square) — VI I 4 (copy diamond) 

V 2 (copy square) — X 2 (draw design) 

VIII3 (repeat days) — IX 4 (repeat months) 

VIII5 (repeat 5 digits) — X 3 (repeat 6 digits) 

X 3 (repeat 6 digits) — Xlli (repeat 7 digits) 

In applying probable scores for these pairs of tests there is a 
strong presumption that if the first of a pair is minus the second 
will be minus, and that if the second is plus the first will be plus 
because of psychological similarity of test-problems. There is, 
however, technical objection on the grounds of incomplete iden- 

5 For a description of the i-year and 2-year tests see (2) pp. 45 ff. For 
a description and arrangement of the Goddard Binet Scale as a whole see 
(13). 



36 EDGAR A. DOLL 

tity to scoring one of the tests of these pairs in terms of the 
other of the pair. This objection finds support in the inconsis- 
tency of reactions sometimes showed in these pairs by epileptic 
or demented subjects. Yet we shall commit no serious practical 
error in formulating a rule analogous to part (a) of Rule 3. 
One might also develop a favorable argument for applying part 
(b) of Rule 3 to these pairs on the ground of the admitted 
tendency of examiners to ignore probable plus scores in the low- 
er ranges and to ignore probable minus scores in the upper ranges. 
We prefer, however, to err in the direction of conserva- 
tism on this point and therefore admit part (a) of Rule 3 but 
exclude part (b) in scoring the pairs under this Rule 4. There- 
fore we state Rule 4 as follows: 

If the first of the above pairs is scored minus, the second if 
unscored is to be scored minus ; and if the second is scored plus, 
the first if unscored is to be scored plus. 

Rule 5. — In the case of tests showing lesser degrees of de- 
pendence than the pairs listed under Rule 4 it is necessary to ap- 
peal to the usual performance or typical score in a test in a suc- 
cession of examinations. In the case of the feeble-minded this 
criterion is fairly dependable, since there is a remarkable degree 
of similarity between successive examinations, not only in the 
gross mental ages but in the individual tests. Our rule on this 
point, however, may not properly be based on an assumption of 
such similarity, since the investigation of this alleged similarity 
is our fundamental problem. Hence we must formulate a rule 
which while it assumes a tendency toward such similarity for 
brief periods does not assume it for long periods of time. We 
cannot, in other words, afford to ignore a possible influence of 
age or experience which may affect the successive reactions to in • 
dividual tests. We have adopted the following rule as affording 
a maximum of satisfaction and a minimum of objections : 

(a). If in a series of examinations an unscored test is sur- 
rounded by at least three or more recorded plus scores (two be- 
fore and one after, or vice versa) without intervening minus 
scores, such unscored test is to be scored plus. And similarly 
for minus. 



THE GROWTH OF INTELLIGENCE 37 

Examples:" + +( + )+;+(+)++;—(—) 

(b). An unscored test prior to the first recorded score is to 
be (i) scored plus when the first two recorded scores are plus; 
(2) scored minus if the first recorded score is minus; and (3) 
scored plus and minus (half credit or .1 year) if the first two 
recorded scores are a plus followed by a minus; provided that 
if the upper range of tests becomes extended in successive ex- 
aminations because of increase in mental age then the unscored 
tests which precede the initial score for that test are to be scored 
minus (in the upper range) regardless of subsequent pluses. 
Examples: (1) ( + ) + +; (2) (— ) — +; (3) (±) + — 
(c). If in a succession of scores which are sometimes plus and 
sometimes minus an unscored test is surrounded by three unlike 
signs (two plus and one minus, or vice versa) such unscored test 
is to be (1) scored plus if 75 per cent or more of all scores re- 
corded for that test are plus; (2) scored minus if less than 25 
per cent of all recorded scores are plus; and (3) scored plus 
and minus if between 25 per cent and 74 per cent, inclusive, of 
all recorded scores are plus. For this section of this Rule to be 
operative the test in question must have been scored in at least 
50 per cent of the total number of examinations. Scores sup- 
plied in accordance with Rules 3 and 4 above are to be considered 
as recorded scores for purposes of this Rule. 
Examples: (1) + + + +( + ) — + + — + 
(2)— +(— ) + 

(3) +- + + (±) + 

Rule 6. If a test has been scored in less than 50 per cent of 
the total number of recorded examinations such test is considered 
an 'isolated test.' Unrecorded scores of an isolated test are to 
be (a) scored plus if all recorded scores for that test are plus 
(b) scored minus if all are minus, (c) If some recorded scores 
are plus and some are minus, then the actual score as recorded is 
to be discarded and the test is to be scored (1) minus in the 
upper range, (2) plus in the lower range, and (3) plus and 
minus in the middle range, provided that if the lack of recorded 

6 The symbols in parentheses indicate test-scores which have been supplied 
under the objective rules for scoring incomplete examinations. 



38 EDGAR A. DOLL 

scores occurs in the early examinations and an extension in the 
upper range of tests is made necessary by significant increase in 
mental age, then (i) prior to the first recorded score the un- 
scored test is scored according to Rule 7, and (2) after the first 
recorded score it is scored according to sections a, b and c of 
Rule 5. 

Rule 7. Unscored tests in the lower range (of each examina- 
tion) are presumed as plus, in the upper range as minus and in 
the middle range as plus and minus. This Rule applies only 
after all preceding rules have been applied. 

These rules were formulated after a minute analysis of the 
problem. They were, with others, tried experimentally before 
being adopted, being checked against the more or less obvious 
probabilities of combined considerations. These particular rules 
seemed to meet all necessary considerations on a strictly objec- 
tive basis and at the same time seemed to avoid any assumptions 
which might bias the results or introduce a constant error. In- 
deed, it is felt that the rules are more elaborate and specific than 
the nature of the error to be corrected may warrant. For it 
should be emphasized that the omissions were neither very fre- 
quent nor very serious. In deciding upon the rules a bias was 
maintained for a tendency to score minus in the upper range 
and plus in the lower range. Hence, there is no obscuring of 
significant progress. It should also* be emphasized that the cor- 
rections to the gross mental ages were always slight. 

The critical student may question our choice of pairs of tests listed under 
Rule 4. It will seem to him, according to his own analysis of the meaning 
of the individual Binet tests, that some tests are improperly included and 
that other pairs are improperly omitted. Indeed, our original list was sup- 
plemented by a second list of eighteen additional pairs of tests which seemed 
to contain the same fundamental psychological elements, but this second 
list has been omitted from our rules because of lack of sufficient identity 
in the test-problems. This list included such pairs as memory for sentences 
and memory for numbers, comparing lines and comparing weights, 
adding stamps and making change, and so on. In these pairs, however, the 
specific problems were not so similar as in our other list and the reaction 
to one of the pair did not include reaction to the other. 

We also considered the possibility of supplying scores solely on the basis 
of known association of successes or failures in pairs of tests. This principle 
was discarded because of insufficient data and individual variability. This 



THE GROWTH OF INTELLIGENCE 39 

criterion breaks down at the crucial places where its usefulness is most 
needed. 

An objection may also be raised to our definition and use of 'range.' This 
objection would be grounded on the contention that the single tests are not 
properly located in the scale in order of serially increasing difficulty. This 
contention is further strengthened by the demonstrated fact that such an 
order of difficulty is not the same for feeble-minded as it is for normal 
subjects (cf. 7). While admitting the truth of these arguments we deny 
their force, for relocation of the tests either for normals or defectives does 
not cause a shift in any test of more than one year. It seemed therefore 
unnecessary to allow for this error. To have done so would have in any 
case been a very difficult matter and the anticipated results did not promise 
to justify the large amount of clerical work involved. 

We offer these rules, then as being sufficiently accurate for 
their avowed purposes. They may be summarized as follows: 

Rule 1. Discard an entire examination if less than 5 tests are 
recorded above highest year where all are passed. 
Rule 2. Credit extra test at year IV : 
(a), plus if 3 or 4 are plus 
(b). plus and minus if only 2 are plus 
(c). minus if less than 2 are plus. 
Rule j. Automatic credit in following pairs: 
III 4 -VII 2 VI 2 -IX 2 

V4-VII, X 5 -XI 2 

(a). If first is minus, score second minus. If second is plus, 
score first plus. 

(b). If first is plus, score second minus (if unscored). 

If second is minus, score first plus (if unscored). 

(c). Correct obvious error by usual performance. 

Rule 4. Automatic credit in following pairs : 

Ii - I 3 and above IV 3 - VIII 5 

I 3 - Hi V 2 - VII 4 

I 3 - H 2 V.- X 2 

Ilia - VI 4 VIII3 - IX 4 

III.- V 3 VIII,- x 3 

III. -IV, X 8 - Xlli 

(a). If first is minus, score second minus (if unscored). 
(b). If second is plus, score first plus (if unscored). 
Rule 5. Usual performance : 



4 o EDGAR A. DOLL 

(a). Score same as three surrounding like signs. 

(b). Prior to first recorded score (i) score plus if first two 
recorded scores are plus, (2) score minus if first recorded score 
is minus, (3) score plus and minus if first recorded score is plus 
followed by minus. Except that if a shift in range is caused by 
change in mental age (1) score plus in lower range, (2) score 
plus and minus in middle range, (3) score minus in upper range. 

(c). If score is surrounded by unlike signs, (1) score plus 
if at least 75 per cent are plus, (2) score plus and minus if 25 
to 74 per cent are plus, (3) score minus if less than 25 per cent 
are plus, provided test is recorded in 50 per cent of examinations. 

Rule 6. In isolated tests (recorded in less than half exami- 
nations) : 

(a). Score plus if all recorded scores are plus. 

(b). Score minus if all recorded scores are minus. 

(c). If recorded scores are plus and minus ignore recorded 
score and score test throughout series ( 1 ) minus in upper range, 
(2) plus and minus in middle range, (3) plus in lower range, 
unless, 

(d). If mental age increases, score minus prior to first re- 
corded score, or score according to parts a, b and c of Rule 5 
after first recorded score. 

Rule 7. Range. Score minus in upper range, plus and minus 
in middle range and plus in lower range when other rules fail 
to provide score. 

Treatment of original material.' — The original records, that is 
the series of successive examinations for each subject, were care- 
fully checked over for completeness in range of testing. Com- 
pleteness in range of testing for each examination was effected 
by supplying scores for unscored tests in accordance with the 
above objective rules. The mental age for each examination was 
then calculated by adding to the lowest year where all tests were 
passed one year for each additional five tests passed. The cor- 
responding life age of each subject was then calculated for each 
examination. 

As was to have been expected from the conditions under which 
the data were obtained, the time-interval between examinations 



THE GROWTH OF INTELLIGENCE 41 

was not constant. In order to avoid the difficulty of treating the 
material with a variable time-interval it seemed desirable to 
standardize the time element. To accomplish this would very 
greatly reduce the labor of calculating the data, would simplify 
the interpretation of results and would make possible a presenta- 
tion of the essential facts in small compass. The impossibility 
of presenting tabulations of the 1800 individual mental ages 
which form the basis of the study is readily comprehended. 

Minor variations in successive mental ages also suggested the 
inadvisability of plotting growth curves based on single mental 
age determinations. There is an experimental error in every 
single measurement of mental age. 7 This is a complex result of 
unavoidable variability in experimental conditions such as time 
of day, attitude of the subject, attitude and personality of the 
examiner, technical expertness of the examiner, and so on. In 
a succession of examinations this error gives mental ages which 
are sometimes slightly too high and sometimes slightly too low. 
If one takes the average of two or more mental ages there is a 
tendency for these experimental errors to offset each other. 
When the time-interval between examinations is sometimes long 
and sometimes short one is unable to discover whether a mental 
age change is really significant or whether it is a chance varia- 
tion. 

In order to standardize the time-interval between examina- 
tions and at the same time minimize these minor yet sometimes 
misleading fluctuations in mental ages it seemed best to 'smooth' 
the growth records. 8 Experimental statistical treatment of typical 

7 This "error" is more annoying or confusing than serious. In our 1800 
examinations the greatest variability between any two successive examina- 
tions, however close together, is never greater than 1 year of mental age. 
The typical variability is about 2 tests, or .4 years, plus or minus. The in- 
fluence of practice or experience in the successive examinations is prac- 
tically negligible even when the examinations are frequently repeated at close 
intervals, except for a slight spurt in the early mental ages of young "im- 
proving" subjects. This fact is so obvious from inspection of the detailed 
records that we have felt justified in omitting the statistical data. 

8 It need hardly be stated that this smoothing process is a legitimate sta- 
tistical device frequently employed to clarify the interpretation of material 
of this nature. 



42 EDGAR A. DOLL 

cases indicated that the best smoothing was to be obtained by- 
calculating two-year averages of the successive mental ages. It 
has been noted that some subjects were examined several times 
in a single year. In other cases the time-interval was sometimes 
greater than a year (cf. Table i). It was therefore undesirable 
to use a one-year average, since this would sometimes be based on 
several tests, sometimes on one test and sometimes would be 
lacking. A three-year average, on the other hand, effected too 
much smoothing and tended to obscure fluctuations in mental 
age which might be significant. But by averaging all the mental 
ages within a period of two years no significant variation in 
mental age was obscured and at the same time at least two mental 
ages were averaged. This procedure had the additional merit of 
furnishing age intervals of a single year, which furnishes a con- 
venient basis for further calculations. 

To effect these averages all mental ages between the beginning 
of one year and the end of the next year inclusive (from 8.0 to 
9.9 for example) were added together and the sum divided by 
the number of examinations for the period. This average was 
then employed as the 'true' mental age for the mid-point of the 
life age period (9.0 in the above example). Hence every mental 
age was used twice in obtaining the 'true' mental ages. For ex- 
ample, a detailed record of one case shows the following typical 
succession of observed mental ages: 



Mental Age 


7.0 

8.8' 

7.6. 


6.4 

9-3' 
7 .6 


7.2 

9-4 


7.2 
9.9' 

7.6. 


74 

10.5' 

8.4 


6.8 


7.6 


Life Age 


10.6 
8.2 


10.8 
8.2 



; etc. 
11.0 11.3 12.0' 12.4 13.3' 13.4 13.9 

The 'true' mental ages, obtained by averaging from the begin- 
ning of each year to the end of the next year are (approximating 
nearest decimal) : 



Mental Age ;o ?Q ?l ?A y? 



etc. 



Life Age 9.0 10.0 11.0 12.0 13.0 

Here it will be seen that the second series shows an orderly in- 
crease in mental age which is slight but constant in trend, a ten- 
dency which is obscured in the variability of the first series. 



THE GROWTH OF INTELLIGENCE 43 

In those subjects where there was a gap of one year or two 
years between recorded mental ages the method employed con- 
sisted in supplying an hypothetical mental age by means of the 
average from the mental ages immediately preceding and fol- 
lowing the gap. This hypothetical mental age was then used as 
if it were an observed mental age and an average obtained from 
its use as in the preceding description. For example, a record 
shows the following ages (taking only a section of the record) : 

Mental Age 7.8 8.2 7.8 7.8 

— • • 1 • • etc. 

Life Age 21.6 22.0 25.7 25.9 

The age-gaps to be supplied here are for ages 23 and 24 and 
are obtained by averaging the mental age (8.2) at age 22 with 
the mental age (7.8) at age 25. This gives hypothetical mental 
ages of 7.9 for ages 23 and 24. These are then averaged as if 
they were observed mental ages, giving the series (approximat- 
ing to nearest decimal) : 

Mental Age 8.0 8.1 7.9 7.8 

— • ■ — 1 — • • etc. 

Life Age 22.0 23.0 24.0 25.0 

It should be noted that 30 of the 37 subjects where gaps of 
2 years were supplied were over 15 years of age, and that the 
other 7 subjects were all below mental age 7. They are conse- 
quently (as will be shown) subjects whose mental levels were 
not changing except for slight fluctuations plus or minus. Hence 
the error of supplying these intermediate mental ages is not 
great. 

No attempt was made to calculate the exact average life age 
on which the average mental ages were calculated. This entails 
a certain slight error in the tabulations to be presented and in- 
troduces a slight error into subsequent calculations. On the aver- 
age, however, there is no error and the error even at its worst 
cannot exceed a half year of age. For all practical purposes this 
slight error is negligible and its harmless presence is more than 
justified by the facility with which the data may be presented if 
it is ignored. 

Having adopted this method of averaging mental ages we are 
obliged to discard from our final tabulations the single men- 



44 EDGAR A. DOLL 

tal ages of the first year and the last year for each subject. The 
first year's mental age or the average of the first year's mental 
ages would be based on fewer measurements than for the other 
ages, and would be based on a shorter period. Moreover, the 
time-interval from the first year's measurements to the first 
'true' mental age would be a half-year as compared with the 
whole-year interval at other points. And similarly for the last 
year's mental ages. Therefore, in order to avoid the error of 
employing single mental ages at the first and last year (while 
averages would be used in between) and to avoid the use of 
half-year intervals the measurements of the first year and the 
last year of the total period covered are not represented in the 
final tabulations, except as they influence the first and the last 
'true' mental ages which constitute the final basis of the investi- 
gation. 

Tabulation of data. — The tabulation of data is restricted to 
the average mental ages (obtained as described above) of 203 
subjects at average intervals of one year. For every subject 
these averaged mental ages cover a period of at least 3 years, 
representing at least five annual examinations. 

The initial ages of the subjects range from 6 years to 66 
years. Their mental ages range from 1 year to 10 years. The 
subjects include both sexes, but no attempt has been made to 
study sex differences. The proportion of males to females is 
about 3 to 1. 

Classification of the data and subsequent statistical treatment 
is rendered exceedingly difficult by the nature of the experimental 
problem. In a preceding discussion we have presented the con- 
siderations which led to the formulation of the problem. Briefly 
restated the problem is to determine: (1) the relation between 
the age of arrest and final mental age level; and (2) the rela- 
tion between rate of mental age increase and final mental age 
level. 

The adequate solution of these two problems is very seriously 
complicated by the wide range in the ages of our subjects. Yet 
this wide range is needed in order ( 1 ) to cover a sufficiently ex- 
tended life period, and (2) to determine whether increased age 
brings about a mental age decrease, or loss of intelligence, late in 



THE GROWTH OF INTELLIGENCE 45 

life. The problem is further complicated by the relatively small 
number of cases which have been examined for long periods of 
time. 

The most satisfactory classification of the data is one based 
on the final mental age, or the terminal intelligence level of the 
subjects. It is possible from the data to determine this terminal 
level with a very fair degree of certainty. Displacement of an 
individual subject in this classification is seldom greater than a 
half year even when allowance is not made for minor fluctuations 
in the exact final mental age. This principle of classification has 
been adopted for the following reasons : 

i. It is not possible to classify by the initial mental ages. The 
subjects are feeble-minded persons who have been sent to an 
institution not because of a particular age or mental age but be- 
cause they were believed to be feeble-minded or potentially feeble 
minded. They have been accepted at the institution on the basis 
of clinical diagnosis which confirmed that belief. Hence the 
exact mental ages at the time of first examination are mere ac- 
cidents. They represent merely the intelligence of the patients 
when they happened to come under observation. In some cases 
the mental retardation has been very great (in the case of the 
older subjects), in others it has been slight, and in a few others 
(the potentially feeble-minded) it has been practically zero. This 
makes it impracticable to classify subjects on the basis of initial 
mentality. Moreover, as we shall show later, this classification 
does not lend itself to an adequate analysis of our problem as 
formulated. 

2. It also seemed desirable to classify the subjects according 
to life ages at the first examination. This would have made 
possible a measure of progress at each life age. But this classi- 
fication was made impossible by the small numbers of subjects 
and the unequal numbers of subjects at each age, and by the 
variations in mental ages at each life age. This latter factor in- 
troduced an influence of unequal weighting that was undesirable. 

3. If we could have eliminated one of the two factors of age 
and mental age by means of some intelligence ratio our problem 
would have been relatively simple. The intelligence quotient 
(I. Q.) is frequently used for this purpose. But the use of the 



46 EDGAR A. DOLL 

I. Q. involves two preliminary assumptions, namely, (i) that the 
level of arrest is independent of the age of arrest (the level be- 
ing reached at about 16 years of age), and (2) that the rate of 
development is a constant for all types as well as all degrees of 
intelligence deviation (idiots excepted). Unless we were willing 
to make these assumptions we could not use the I. Q. as a basis 
of classification in this study. An I. Q. of 50, for example based 

Mental Age 4 

on the ratio = — , would not be the same as its 

Life Age 8 

Mental Age 8 

equivalent ratio of 1 = — . Moreover, variations in 

Life Age 16 

I. Q. are obscured by the fact that increases or losses in mental 

age must be spread over the entire earlier ages of the subjects 

instead of simply the time-interval between examinations. 

We cannot accept these two assumptions of the I. Q. in this 

study, for it is these assumptions themselves which form the 

basis of our investigation. In fact our data will disprove both 

of these assumptions as applied to feeble-minded subjects. 

4. For the same reasons we cannot employ years of retarda- 
tion as a basis of classification. An increase in years of retarda- 
tion after the age of arrest is a mere accident of the length of 
time which has elapsed since that date. Hence if age of arrest 
is dependent upon level of arrest we cannot employ years of re- 
tardation for present purposes. 

5. We have made an earnest endeavor to devise an intelligence 
ratio which would be unaffected by assumptions such as those 
which invalidate the I. Q. but have been obliged to confess in- 
ability to devise such a ratio. The problem seems insoluble in 
view of the known facts. 

6. The classification based on the final mental levels of the 
subjects is unobjectionable and it exactly serves the purposes of 
our investigation. 

To effect such a classification it is necessary to establish a suc- 
cession of mental ages which do not materially increase or de- 
crease except for slight fluctuations above and below a final 
level. Having determined this level the second problem is to 
determine at what age this level was first reached. The third 



THE GROWTH OF INTELLIGENCE 47 

problem is to determine the annual mental age increments by 
which the level was reached. The degree of success with which 
it is possible to determine the final mental level may be judged 
from the tabulations of averaged mental ages, for we present the 
material in full (cf. Table 2) in such form that anyone may plot 
the actual curves of growth. 9 

Our method has been to draw the individual growth curves of 
each subject and then by inspection to determine the point at 
which each curve reaches an approximate level. But this may be 
done almost as readily by inspection of Table 2. It will be seen 
that with only a few exceptions the mental level is easily de- 
termined by inspection. Only 19 per cent of all cases show a net 
increase in mental age of as much as 1.0 year or more within a 
period 3 to 5 years. In all but one instance these are subjects 
who are below 15 years at the initial life age. They represent 
38 per cent of all subjects under that age. Only 6 subjects, or 
3 per cent, have gained as much as 2 years of mental age in 4 
years of life age, that is after 5 annual examinations. In other 
words, 97 per cent of all subjects have mental levels which have 
increased by less than 2 years after 5 annual examinations. 

In classifying the subjects in final mental age groups we have 
chosen the mental age year-interval within which the majority 
of fluctuations in level fall. The limits of a group include from 
the beginning of a mental year to the end of that year, for ex- 
ample 5.0 to 5.9 inclusive. An occasional subject might be dis- 
placed by a small fraction of a year above or below classification 
limit. He will never be displaced by as much as a half year. 

Cumulative mental age increases. — The experimental material 
is presented in Table 2. This table is designed to show the total 
amounts of increase in mental age for each subject after 1 year, 
2 years, and so on of re-examining. The subjects are classified 
according to final mental age levels and are arranged in order of 
life ages within each mental age group. 

9 It is not possible to publish the complete data of the 1800 individual 
mental ages except in this fashion. The original material of the investiga- 
tion may be obtained from The Training School at Vineland, N. J., for 
limited periods of time by responsible students who may desire to examine 
critically the method of treatment here employed. 



EDGAR A. DOLL 



Table 2* 

Increases of mental age in repeated Binet tests; 203 feeble-minded subjects 
classified by final mental age level. 
Section A — Final mental age 1 year 





First 


First 




Q 


lmulativ 


e mental age 


increases 


Subject 


life 


mental 


after 


after 


after 


after 


after 


after after after 


No. 


age 


age 


1 yr. 


2 yrs. 


3 yrs. 4 yrs. 


5 yrs. 


5 yrs. 7 yrs. 8 yrs. 


1 


10 


1.7 





.2 


•3 


.2 


.1 




2 


12 


1-3 


.1 


.2 


•3 








3 


13 


1.0 




















4 


13 


1-7 


.2 


•3 


•3 


•3 


_2 


.1 


5 


14 


1-4 


—•4 


— .2 


.1 








6 


19 


1.0 





.1 


•3 


•3 


•3 


•3 






Section B- 


—Final mental 


age 


2 years 




7 


8 


3-1 


•7 


.6 


.2 


—.2 


—•5 




8 


8 


2.7 


.2 


•4 





—.2 


— .1 


•3 


9 


8 


2.0 


















10 


9 


1.8 


.1 


•3 


•4 


•3 







11 


11 


2.8 


.2 


.1 


— .1 





.1 




12 


11 


2.2 


.2 


.2 


.2 


.2 






13 


13 


2.0 








— .1 








14 


23 


2.4 














— .1 








Section C- 


—Final mental 


age 3 years 




IS 


6 


2.6 


— .1 


•3 


•7 








16 


7 


3-6 





•4 


.2 








17 


9 


3-4 





.1 


.1 


.1 


.1 




18 


11 


43 


.2 


.1 





—.6 


—.7 




19 


12 


3.o 


.2 


.6 


•4 


•4 


•3 




20 


IS 


2.8 





— .1 





•3 


.6 




21 


15 


3-2 


— .2 


—•3 


— .2 









22 


16 


3-8 





— .1 


— .2 





— .1 




23 


20 


3-5 


.1 


•3 


-3 


.2 


.1 


— .1 — .1 


24 


25 


3-8 


.6 


•3 


— 4 


-•4 


—•3 


— .2 


25 


29 


3-5 


.1 


.1 





—.1 


— .2 


—•3 


26 


32 


3-8 


•5 


•5 


•4 


— .1 


—•3 


— .2 


27 


34 


2-9 


■3 


•5 


•3 


.2 


.2 


.2 






Section D- 


—Final mental 


age 4 years 




28 


8 


3-3 


•9 


1.1 


1.1 


1.0 


1.2 


1-5 


29 


11 


3-6 


•3 


•4 


.2 


.2 


•4 


.6 .9 


3o 


11 


4-3 


# 2 





.1 








31 


12 


3-9 


.1 


•4 


•3 


.2 


.1 


— .1 


32 


12 


4.4 


O 


— .2 


—•5 








33 


12 


4-7 


.1 


— .1 


.2 


_2 






34 


14 


3-8 


•3 


•4 











35 


14 


3-9 


•4 


•3 





.1 


•4 


•5 -3 


36 


15 


4-5 


.2 


.1 


.1 








37 


16 


3-9 


•5 


.6 


•4 


•3 


.2 




38 


17 


4-3 


.1 


•3 


.2 


— .1 


.2 


•3 


39 


21 


4.0 


.2 


•4 


•3 


•4 


•5 


•3 


40 


22 


4-7 





.1 


— 3 








4i 


22 


4.6 


•7 


1.0 


.6 


•3 


.2 


.1 


42 


37 


4-5 








—.1 


— .1 


—.1 




43 


45 


46 


— .2 


— .1 












* For explanation of table see p. 52. 



THE GROWTH OF INTELLIGENCE 



49 



Table 2 (continued) 
Section E — Final mental age 5 years. 





First 


First 




Cumulative mental age 


increases 




Subject 


life 


mental 


after 


after 


after 


after 


after 


after 


after 


aftei 


No. 


age 


age 


1 yr. 


2 yrs. 


3 yrs. 


4 yrs. 


5 yrs. 


6 yrs. 


7 yrs. 


8 yrs 


44 


7 


3-7 


.1 


.2 


•4 


1.2 


1.7 


1.9 


2.0 


2.0 


45 


9 


3-6 


1.0 


1.6 


2.3 


2-3 










46 


12 


4-3 


.2 


•4 


•5 


•7 


•9 


1-3 






47 


12 


4-5 


.2 


•3 


•5 


.6 


■7 








48 


12 


5-6 


.2 


•3 


•3 


.3 


•3 








49 


13 


5-1 





— .1 


— .2 


— .1 










50 


16 


49 


.6 


.8 


.8 


.8 


•9 








51 


16 


4-9 


•4 


.6 


•3 


•3 


•4 


•4 






52 


16 


5-5 


.2 


.2 











.1 






53 


17 


4.9 


.1 


.2 


.2 


.2 


.2 








54 


18 


4.9 


•4 


•5 


•3 


•3 


•3 








55 


19 


5-3 


.2 


.8 


.8 


•5 










56 


26 


5-2 


.2 


•3 


•3 


.2 


.1 








57 


29 


4-8 


•3 


•4 


.2 


.2 


•5 


•4 


.1 


.2 


58 


30 


6.5 


—•4 


.1 


—.8 


— 1.0 










59 


36 


5-9 





— .1 


—•5 


—.8 


— 1.0 


— i.i 






60 


66 


5-9 


•3 


.2 


— .2 


— 3 


— 4 












Section F- 


—Final mental age 


6 years 








61 


8 


3-8 


•4 


1-3 


1-7 


2.1 


2.3 


2.4 






62 


8 


4.0 


•3 


i.i 


1-3 


i-5 


1.8 


2.0 


2.2 




63 


9 


4-5 


.8 


1-5 


1.6 


1.2 


i-5 


1.6 


1.7 




64 


10 


6.2 


.1 


.2 


•4 


•5 


•7 








65 


11 


5-9 


•4 


•4 


•4 


.1 










66 


11 


6.4 


•5 


•7 


•7 


.8 


.6 


•4 


•5 


•5 


67 


12 


5-1 


•9 


1-4 


1-3 


1.6 










68 


13 


5-2 


.6 


•7 


•5 


•7 


.8 


•9 


1.0 




69 


15 


6.3 


.2 


•3 


.6 


.6 


.6 


•5 


•4 


•5 


70 


15 


6.4 


•3 


•4 


•4 


•4 


•4 


■3 


O 




7i 


15 


6.4 


.1 


.1 


.1 














72 


15 


6.7 


— .1 


— .2 


— .2 













73 


16 


6.1 





— .1 


O 


•3 


•3 


_2 


.1 





74 


17 


6.1 


.2 


•4 


O 


— .1 


— .2 








75 


20 


6.4 


■3 


•4 


O 


— .1 


.2 


•3 


.1 


— .1 


76 


22 


6.0 


.2 


•4 


•3 


.2 


,.1 


1 






77 


23 


6.8 


•3 


.2 


.2 


.1 


— .1 


— .2 


— .2 


— .1 


78 


26 


6.3 


•3 


.2 


.2 


•3 


•4 


•5 


•3 




79 


26 


6.6 


— .1 


O 


— .1 


—•4 


— .2 


— .1 


—•3 


— .1 


80 


29 


6.7 


— .2 


— .2 





.1 


.1 


— .1 






81 


30 


6.4 


.1 


•3 


.2 












82 


32 


6.0 


.1 


•3 


•4 


•4 


.1 


.1 


•3 




83 


32 


6.5 


— .2 


— .1 


— .1 


— .1 


— .1 








84 


35 


5-9 


•3 


•4 


•5 


•5 


■5 


•4 






85 


37 


6-3 


•7 


•7 


.2 








.1 











Section G 


— Final mental age 7 years 








86 


7 


4.9 


1.1 


1-5 


2.0 


2.0 


2.0 


2.4 






87 


7 


5-6 


•4 


•7 


I.I 


1.2 


1.4 


1-7 






88 


7 


5-7 


I.i 


1-4 


1.8 


1.9 


1.8 








89 


7 


57 


.8 


i.i 


1.3 


i-7 


1.8 








90 


8 


4.4 


i.i 


1.8 


2.2 


3-1 


3-i 


3-2 






9i 


8 


4-5 


1.0 


i-5 


2.2 


2.4 


2-5 


2.5 


2.6 


2.8 



5o 



EDGAR A. DOLL 









Table 2 


(continued) 










Section G- 


—Final 


mental age 


7 years (continued) 






First 


First 




Cumulative mental age 


increases 


Subject 


life 


mental 


after 


after 


after 


after 


after 


after 


after after 


No. 


age 


age 


1 yr. 


2 yrs. 


3 yrs. 


4 yrs. 


5 yrs. 


6 yrs. 


7 yrs. 8 yrs 


92 


8 


5-5 


.2 


.8 


1.1 


1.6 


2.0 






93 


8 


5-9 


.8 


1.2 


1.1 


1-3 


1.4 






94 


8 


6-3 


•5 


.8 


1.2 


1.4 


1.2 


1.4 




95 


9 


4-3 


•7 


1-5 


2.4 


2.8 


3-0 


3-0 


3.0 2.8 


96 


9 


6.6 





.1 


.1 


•3 


.8 


1.0 




97 


9 


6.7 


.6 


•7 


.6 


1.0 


1.2 






98 


10 


7.0 


.1 


.2 


•3 


•5 


•5 


•3 


3 


99 


10 


7-3 


— .2 


— .2 


.1 










100 


n 


5-9 


.6 


•7 


1.3 


1.6 


1.6 






101 


11 


7.0 


.1 


.1 


.1 


.1 


.1 


.1 




102 


11 


7.2 


.1 


•5 


•7 


•5 


•4 






103 


12 


6.9 


.6 


•7 


•7 










104 


13 


6.0 


•7 


1.1 


1.1 


1.1 


1.1 


1.1 


1.0 .9 


ios 


13 


6.4 


•5 


•4 


•4 


1.2 


1-3 






106 


13 


6-5 


.2 


•4 


•5 


•5 


•5 






107 


13 


6.6 


•3 


•5 


•7 


•7 


.2 


.1 




108 


13 


7-3 


.2 


.1 


•5 


.6 








109 


13 


7-8 


•5 


•5 


•5 


•3 


.2 








no 


14 


6.9 


•4 


•5 


•7 










III 


14 


6.7 


•5 


•4 


•4 


•5 


•5 






112 


14 


7-5 




















113 


15 


7-2 





.2 


•3 


•5 








114 


16 


7-1 











— .2 


.2 


•5 


.4 .4 


115 


17 


7-7 





— .1 


.1 





— .1 






Il6 


19 


6.7 


•3 


•5 


•5 


•4 


•4 


•4 




117 


19 


7-5 


•3 


.2 


.1 


.1 





— .1 




Il8 


20 


7-4 


.1 


.2 


.2 


.2 


.2 






119 


20 


7-5 


.1 


•4 


•4 


•3 


.1 


.2 


•3 


I20 


20 


7-6 


•3 


•4 


•5 


•3 


.2 


.1 





121 


20 


7-7 


.2 


•5 


•4 


■3 


.2 


.2 


.1 


122 


22 


7-8 


•5 


•5 


.1 


— .1 


— .2 


— .1 


•3 


123 


26 


7-8 


.2 


.2 


.1 


.1 


.2 






124 


28 


7-5 


.2 


— .1 


— .1 


.1 


.1 






125 


28 


7-7 


.2 


•3 





— .1 


— .2 






126 


30 


7.6 





•5 


.8 


•5 


•3 


— .2 




127 


31 


8.4 


— .2 


— .2 


—•3 


—•5 


—.6 


—.6 




128 


34 


7-7 


— .1 


— .2 





.2 





— .2 


— .1 


129 


36 


7-6 


—•4 


—•4 


—•3 


—•3 


— .2 


—•3 


—•5 


130 


36 


7.2 


— .1 

















131 


38 


7.0 


.1 


.2 


.1 


.1 


.2 


.2 








Section H- 


—Final mental age 


8 years 






132 


8 


6.6 


.6 


1.0 


1.3 


1.4 








133 


8 


7.0 


.2 


•4 


.6 


•7 


1.1 


i-5 




134 


8 


7-3 


.8 


•9 


•9 


•7 


.8 


•9 


•9 


135 


9 


7.0 


.1 


•4 


•7 


1.0 


1.2 


•9 


1.2 1.4 


I36 


9 


7.2 


•3 


•5 


•7 


.8 








137 


10 


7-1 


•5 


■7 


1.0 


1.2 


1-5 


1.6 


1.4 


138 


10 


7-6 


.8 


•9 


1.0 


1.0 


1.2 






139 


10 


7-8 


.6 


•7 


•7 


•9 








I40 


13 


7-9 


.2 


.2 


.2 


.6 


■5 


•7 




141 


14 


8.0 





.1 


.2 


•3 










THE GROWTH OF INTELLIGENCE 



Si 





Section H 


— Fina 


mental age 


8 years (continued) 






First 


First 




Cumulative mental age 


increases 


Subject 


life 


mental 


after 


after after 


after 


after 


after 


after after 


No. 


age 


age 


1 yr. 


2 yrs. 3 yrs. 


4 yrs. 


5 yrs. 


6 yrs. 


7 yrs. 8 yrs 


142 


14 


8.1 





.2 


2 










143 


14 


8.2 


.2 


.1 — 


3 


— .2 










144 


14 


8-5 





— .2 — 


2 


— .1 








145 


15 


8.5 


.2 


•3 


1 


.1 


.2 


•3 


•5 


146 


15 


7-7 





.2 


4 


•3 


•3 


•3 




147 


16 


8.1 


.1 


.2 


2 


.2 


.2 


•7 




148 


18 


7-8 





•3 


4 


.6 


•5 


•4 


•5 


149 


18 


8.9 


•3 


.2 — 


3 


—.6 


—.8 


—■7 


—•4 


150 


21 


8.0 


•3 


.6 


2 











— .1 


iSi 


22 


8.6 


•3 


.2 — 


2 


—.3 


—•3 


— .1 




152 


22 


8.6 


—•3 


—•3 — 


1 


—•3 








153 


23 


8.0 


.1 


•3 


4 










154 


23 


8.6 


.1 


— 


1 


—•5 


—.6 







155 


27 


8.0 





.2 


2 


.1 









156 


32 


8-5 


— .2 


—•3 


4 


.2 


•5 






157 


35 


8.2 


•5 


•4 


1 


.1 


.1 


—•5 




158 


39 


7.8 


.2 


.6 


7 


•9 


•7 


.6 


.4 .4 






Section I- 


—Final mi 


mta 


1 age 9 years 






159 


8 


7-6 


.2 


.4 1 





1.6 








160 


9 


7.0 


•5 


.6 1 





1.3 


1.9 


2.1 


2.2 


161 


9 


7-i 


•3 


.6 


9 


1.1 


1.9 






162 


9 


8.2 


•3 


.8 1 


1 










163 


9 


8.4 


•5 


.8 


7 










164 


10 


9-3 


.2 


.6 


5 










165 


11 


9-1 


.1 


.1 


6 


•7 


•3 






166 


12 


8.4 


.1 


•3 


8 


1.0 


1-3 






167 


13 


7-5 


•5 


1.1 1 


4 


1.4 


1.6 






168 


13 


8.6 


.1 


•7 1 





1.2 








169 


13 


8.9 


•4 


.6 


9 


•9 








170 


14 


8.4 


•4 


•9 1 


I 










171 


14 


8-4 


•3 


•9 1 


2 


1.0 


.8 






172 


15 


8.6 


.1 


.1 


2 


•3 


•5 


•7 




173 


17 


9.1 


— .2 


•3 


7 










174 


17 


9-3 


.2 


—•3 — 


3 










175 


18 


9-5 


— .2 


•4 — . 


3 


— 3 








176 


19 


9.0 








2 










177 


21 


8.8 


.1 


.2 


4 


•4 


•4 






178 


23 


8.9 


•4 


.2 


3 


.6 


.8 






179 


26 


9.4 





— .2 — . 


2 


.1 





— .2 




180 


28 


9.1 


■3 


•9 


8 










181 


30 


9.0 


.2 


.2 


4 


•4 


•3 






182 


30 


9-6 





.2 


5 


•5 


.2 






183 


33 


9.4 


.1 


.2 


3 


•4 


•5 






184 


40 


9-3 


.1 


.1 


1 


.2 


•4 










Section J- 


-Final me 


ntal 


age 10 years 






185 


11 


8.0 


•4 


.8 1. 


3 


1.6 


2.0 






186 


11 


8-5 


•4 


.7 1. 


5 










187 


14 


10.4 





.2 


3 


•4 








188 


16 


9-3 


.2 


.6 


2 





•9 


1.0 


.8 1.1 


189 


16 


9-9 


•5 


•5 


8 


•9 


•5 


•5 


.8 



52 EDGAR A. DOLL 

Table 2 (continued) 

Section J — Final mental age 10 years (continued) 

First First Cumulative mental age increases 

Subject life mental after after after after after after after after 

No. age age 1 yr. 2 yrs. 3 yrs. 4 yrs. 5 yrs. 6 yrs. 7 yrs. 8 yrs. 

190 16 10.5 — .4 — .3 — -I 

191 16 107 .2 .4 .5 .1 .1 

192 17 10.8 .1 .4 .5 .2 

193 18 9.8 .3 .2 .1 .3 .4 

194 19 9.4 .4 1.1 1.4 1.4 1.6 1.1 .9 

195 20 9.9 .2 .5 .3 .4 .7 

196 22 10.0 .1 .1 .1 o — .1 .3 

197 22 10.7 — .3 — .3 — .2 — .1 — .1 

198 24 10.2 o .2 .2 .2 .1 

199 24 10.2 .3 .1 .1 .3 .6 .7 -5 

200 25 10.6 o .2 .5 

201 28 9.8 .4 .6 .6 .6 .5 

202 44 10.5 — .2 — .2 .3 

203 46 9.6 .3 .6 .8 .7 7 

The first column of this table gives the serial number of the subject. 
(These are for convenience of reference only and have no other significance.) 
The second column shows the first average life age of each subject. (This is 
actually the second year of the original data since the first year has been 
lost by the method of averaging the data.) The third column shows the 
first average mental age of each subject. (This is actually the average of 
all records for the first and second years of the original measurements.) The 
succeeding columns from left to right show the annual cumulative increases 
in mental age after the first mental age. (These are obtained by adding the 
increase at each year to the net total increase of the preceding years.) The 
first line of the table reads as follows: subject No. 1 with final mental age 
1 year, first life age 10 years, first mental age 1.7 years, after 1 year had 
gained .0 years in mental age, after 2 years had gained .2 years, after 3 years 
had gained .3 years, etc. The mental ages at each succeeding year may be 
obtained by adding the cumulative increases to the first mental ages. The 
life ages increase regularly by i-year intervals. Thus the first subject just 
cited would have the following mental ages and life ages : 

Mental Age 1.7 1.7 1.9 2.0 1.9 1.8 

Life Age 10.0 11.0 12.0 13.0 140 15.0 

Rate of mental age increase. — The amounts of annual mental 
age increments may be obtained by subtracting each cumulative 
increase from the next succeeding (right-hand) cumulative in- 
crease. For example, subject No. 1 gained in the first year .0, 
in the second year .2, in the third .1, in the fourth — .1, and in 
the fifth — .1. 

The annual mental age increments may be expressed as an 
annual rate of increase by dividing the mental age increment by 
the life age increment. This may be converted to a percentage 



THE GROWTH OF INTELLIGENCE 53 

rate of increase by multiplying by 100. This percentage rate of 
increase must not be confused with or interpreted as a percentage 
of the total mental age. It is a percentage of the average nor- 
mal annual rate of increase by a scale which is so devised as to 
provide for a normal average increase of 1 year in mental age 
for each increase of 1 year in life age up to a given limit of the 
scale or of age. 

These annual rates of increase as percentages of the average 
normal annual rate can readily be calculated from Table 2. But 
for convenience in presenting the argument on rate of increase 
for the feeble-minded, Table 3 is presented to show these rates 
of increase. The succession of cases and the organization of 
the material is the same as that of Table 2. 

Results. — The best analysis of results is obtained from direct 
inspection of Table 2 and Table 3. Statistical devices such as 
expressions of central tendency, coefficients of variability, and 
coefficients of correlation obscure rather than clarify these re- 
sults. We believe that by casting the data in the form of the 
above tables we have achieved a presentation that is much more 
adequate for purposes of exact analysis than is yielded by the 
usual statistical methods. We shall be able by inspection to dis- 
cover trends and variations and at the same time to keep clearly 
in mind the essential characteristics of each mental age period, 
of each life age period, and of each individual subject. We 
shall attempt to formulate certain generalizations on this basis. 

Relation of age of arrest to level of arrest. — The analysis of 
the relation of age of arrest to level of arrest is seriously limited 
by the lack of sufficient numbers of subjects in the younger age 
periods. This lack obscures the relationship which may exist. 
Nevertheless certain trends may be observed as follows : 

1. Substantial increases are limited to subjects who are under 
15 years of age. Only one subject of this investigation (No. 
188) shows as much as one year of permanent increase in mental 
age after the age of 14 years. 

2. Only two subjects show decrease in mental age amounting 
to as much as one year. One of these is 30 years old and the 
other 36 at the first record. Twenty-five other subjects who are 
30 years or older do not decrease. 



54 EDGAR A. DOLL 

Table 3 
Annual rates of mental age increase in repeated Binet tests : 203 feeble- 
minded subjects classified by final mental age level. 
Section A — Final mental age 1 year 



year year 





First 


First 




Successive 


rates c 


if mental a£ 


Subject 


life 


mental 


1st 


2nd 


3rd 


4th 


5th 


6th 


No. 


age 


age 


year 


year 


year 


year 


year 


yeai 


1 


10 


1-7 





20 


10 


— 10 


— 10 




2 


12 


1-3 


10 


10 


10 








3 


13 


1.0 




















4 


13 


i-7 


20 


10 








— 10 


— 10 


S 


14 


1.4 


—40 


20 


30 








6 


19 


1.0 





10 


20 















Section B — Final mental 


age 2 


years 




7 


8 


3-1 


70 


— 10 


—40 


—40 


—30 




8 


8 


2.7 


20 


20 


—40 


— 20 


10 


40 


9 


8 


2.0 


















10 


9 


1.8 


10 


20 


10 


— 10 


—30 




11 


11 


2.8 


20 


— 10 


— 20 


10 


10 




12 


11 


2.2 


20 















13 


13 


2.0 








— 10 








14 


23 


2.4 














— 10 








Section C — Final mental 


age 3 years 




15 


6 


2.6 


— 10 


40 


40 








16 


7 


3-6. 





40 


—20 








17 


9 


3-4 





10 













18 


11 


4-3 


20 


— 10 


— 10 


—60 


— 10 




19 


12 


3-0 


20 


40 


— 20 





— 10 




20 


15 


2.8 





— 10 


10 


30 


30 




21 


15 


3-2 


— 20 


— 10 


10 


20 






22 


16 


3-8 





— 10 


— 10 


20 


— 10 




23 


20 


3-5 


10 


20 





— 10 


— 10 


— 20 


24 


25 


3-8 


60 


—30 


—70 





10 


10 


25 


29 


3-5 


10 





— 10 


— 10 


— 10 


— 10 


26 


32 


3-8 


50 





— 10 


—50 


—20 


10 


27 


34 


2.9 


30 


20 


— 20 


— 10 












Section D — Final mental 


age 4 years 




28 


8 


3-3 


90 


20 





— 10 


20 


30 


29 


11 


3-6 


30 


10 


— 20 





20 


20 


30 


11 


4-3 


20 


— 20 


10 








3i 


12 


3-9 


10 


30 


— 10 


— 10 


— 10 


— 20 


32 


12 


4.4 





— 20 


—30 








33 


12 


4-7 


10 


— 20 


30 









34 


14 


3-8 


30 


10 


—40 








35 


14 


3-9 


40 


— 10 


—30 


10 


30 


10 


36 


15 


4-5 


20 


— 10 











37 


16 


3-9 


50 


10 


— 20 


— 10 


— 10 




38 


17 


4-3 


10 


20 


— 10 


—30 


30 


10 


39 


21 


4.0 


20 


20 


— 10 


10 


10 


— 20 


40 


22 


4-7 





10 


—40 








4i 


22 


4.6 


70 


30 


—40 


—30 


— 10 


— 10 


42 


37 


4-5 








— 10 










43 


45 


4.6 


— 20 


10 


10 









30 



THE GROWTH OF INTELLIGENCE 55 

Table 3 (continued) 
Section E — Final mental age 5 years 

ital age increase 

8th 
year 





First 


First 




Successive : 


rates 


if men 


tal age 


: incr 


Subject 


life 


mental 


I St 


2nd 


3rd 


4th 


5th 


6th 


7th 


No. 


age 


age 


year 


year 


year 


year 


year 


year 


yea: 


44 


7 


3-7 


10 


10 


20 


80 


50 


20 


10 


45 


9 


3-6 


100 


60 


70 











46 


12 


4-3 


20 


20 


10 


20 


20 


40 




47 


12 


4-5 


20 


10 


20 


10 


10 






48 


12 


5-6 


20 


10 















49 


13 


5-i 





— 10 


— 10 


10 








50 


16 


4-9 


60 


20 








10 






5i 


16 


4.9 


40 


20 


—30 





10 







52 


16 


5-5 


20 





— 20 








10 




53 


17 


49 


10 


10 















54 


18 


4.9 


40 


10 


— 20 












55 


19 


5-3 


20 


60 





—30 








56 


26 


5-2 


20 


10 





— 10 


— 10 






57 


29 


4.8 


30 


10 


— 20 





30 


— 10 


—30 


58 


30 


6.5 


—40 


50 


—90 


— 20 








59 


36 


5-9 





— 10 


—40 


—30 


— 20 


— 10 




60 


66 


5-9 


30 


— 10 


—40 


— 10 


— 10 










Section F — Final mental 


age 6 


years 






61 


8 


3-8 


40 


90 


40 


40 


20 


10 




62 


8 


4.0 


30 


80 


20 


20 


30 


20 


20 


63 


9 


4-5 


80 


70 


IO 


—40 


30 


10 


10 


64 


10 


6.2 


10 


10 


20 


10 


20 






65 


11 


5-9 


40 








—30 








66 


11 


6.4 


50 


20 


O 


10 


— 20 


— 20 


10 


67 


12 


5-i 


90 


50 


— 10 


30 








68 


13 


5-2 


60 


10 


— 20 


20 


10 


10 


10 


69 


15 


6.3 


20 


10 


30 








— 10 


— 10 


70 


15 


6.4 


30 


10 


O 








— 10 


—30 


7i 


15 


6.4 


10 








— 10 









72 


15 


6.7 


— 10 


— 10 





20 








73 


16 


6.1 





— 10 


10 


30 





— 10 


— 10 


74 


17 


6.1 


20 


20 


—40 


— 10 


— 10 






75 


20 


6.4 


30 


10 


—40 


— 10 


30 


10 


— 20 


76 


22 


6.0 


20 


20 


— 10 


— 10 


— 10 






77 


23 


6.8 


30 


— 10 





— 10 


— 20 


— 10 





78 


26 


6.3 


30 


— 10 





10 


10 


10 


— 20 


79 


26 


6.6 


— 10 


10 


— 10 


—30 


20 


10 


— 20 


80 


29 


6.7 


— 20 





20 


10 





— 20 




81 


30 


6.4 


10 


20 


— IO 










82 


32 


6.0 


10 


20 


IO 





—30 





20 


83 


32 


6.5 


— 20 


10 


O 












84 


35 


5-9 


30 


10 


10 





— 10 







85 


37 


6-3 


70 





—50 


— 20 





10 


— 10 






Section G — Final mental 


age 7 years 






86 


7 


4-9 


1 10 


40 


50 








40 




87 


7 


5-6 


40 


30 


40 


10 


20 


30 




88 


7 


5-7 


no 


30 


40 


10 


— 10 






89 


7 


5-7 


80 


30 


20 


40 


10 






90 


8 


44 


no 


70 


40 


90 





10 




9i 


8 


4-5 


100 


50 


70 


20 


10 





10 



10 

— 10 

— 20 
10 



20 



56 EDGAR A. DOLL 

Table 3 (continued) 
Section G — Final mental age 7 years (continued) 





First 


First 




Successive rates 


f mental age 


incr 


Subject 


life 


mental 


I St 


2nd 


3rd 


4th 


5th 


6th 


7th 


No. 


age 


age 


year 


year 


year 


year 


year 


year 


yeai 


92 


8 


5-5 


20 


60 


30 


50 


40 






93 


8 


5-9 


80 


40 


— 10 


20 


10 






94 


8 


6.3 


50 


30 


40 


20 


— 20 


20 




95 


9 


43 


70 


80 


90 


40 


20 








96 


9 


6.6 





10 





20 


5o 


20 




97 


9 


6.7 


60 


10 


— 10 


40 


20 






98 


10 


7.0 


10 


10 


10 


20 





— 20 





99 


10 


7-3 


— 20 





30 










100 


11 


5-9 


60 


10 


60 


30 









101 


11 


7.0 


10 



















102 


n 


7.2 


10 


40 


20 


— 20 


— 10 






103 


12 


6.9 


60 


10 













104 


13 


6.0 


70 


40 











• 


—10 


ios 


13 


64 


50 


— 10 





80 


10 






106 


13 


6.5 


20 


20 


10 












107 


13 


6.6 


30 


20 


20 





—50 


— 10 




108 


13 


7-3 


20 


— 10 


40 


10 








109 


13 


7-8 


50 








— 20 


— 10 


— 20 





no 


14 


6.9 


40 


10 


20 










III 


14 


6.7 


5o 


— 10 





10 









112 


14 


7-5 




















"3 


15 


7.2 





20 


10 


20 








114 


16 


7-r 











— 20 


40 


30 ■ 


—10 


115 


17 


7-7 





— 10 


20 


— 10 


— 10 






116 


19 


6.7 


30 


20 





— 10 










117 


19 


7-5 


30 


— 10 


— 10 





— 10 


— 10 




118 


20 


7-4 


10 


10 















119 


20 


7-5 


10 


30 





— 10 


— 20 


10 


10 


120 


20 


7-6 


30 


10 


10 


— 20 


— 10 


— 10 


—10 


121 


20 


7-7 


20 


30 


— 10 


— 10 


— 10 





—10 


122 


22 


7-8 


50 





—40 


— 20 


— 10 


10 


40 


123 


26 


7-8 


20 





— 10 





10 






124 


28 


7-5 


20 


—30 





20 









125 


28 


7-7 


20 


10 


—30 


— 10 


— 10 






126 


30 


7-6 





50 


30 


—30 


— 20 


—50 




127 


3i 


8.4 


— 20 





— 10 


— 20 


— 10 







128 


34 


7-7 


— 10 


— 10 


20 


20 


— 20 


— 20 


10 


129 


36 


7-6 


—40 





10 





10 


— 10 


—20 


I30 


36 


7.2 


— 10 


10 














131 


38 


7.0 


10 


10 


— 10 





10 








Section H — Final mental age 8 years 
132 8 6.6 60 40 30 10 



8th 
year 



—20 



— 10 



133 


8 


7.0 


20 


20 


20 


10 


40 


40 




134 


8 


7-3 


80 


10 





— 20 


10 


10 





135 


9 


7.0 


10 


30 


30 


30 


20 


—30 


30 


136 


9 


7.2 


30 


20 


20 


10 








137 


10 


7-i 


5o 


20 


30 


20 


30 


10 


— 20 


138 


10 


7-6 


80 


10 


10 





20 






139 


10 


7-8 


60 


10 





20 









20 



140 13 7.9 20 o o 40' — 10 

141 14 8.0 10 10 10 — 30 



THE GROWTH OF INTELLIGENCE 57 

Table 3 (continued) 
Section H — Final mental age 8 years (continued) 

increase 

8th 
year 





First 


First 




Successive rates 


E mental age 


incr< 


Subject 


life 


mental 


1st 


2nd 


3rd 


4th 


5th 


6th 


7th 


No. 


age 


age 


year 


year 


year 


year 


year 


year 


year 


142 


14 


8.1 





20 













143 


14 


8.2 


20 


— 10 


—40 


10 


20 







144 


14 


8-5 





— 20 





10 








145 


15 


8-5 


20 


10 


— 20 





10 


10 


20 


146 


15 


7.7 





20 


20 


— 10 










147 


16 


8.1 


10 


10 











5o 




148 


18 


7-8 





30 


10 


20 


— 10 


— 10 


10 


149 


18 


8.9 


30 


— 10 


—5o 


—30 


— 20 


10 


30 


150 


21 


8.0 


30 


30 


—40 


— 20 





- 


—10 


151 


22 


8.6 


30 


— 10 


—40 


— 10 





20 




152 


22 


8.6 


—3o 





20 


— 20 








153 


23 


8.0 


10 


20 


10 










154 


23 


8.6 


10 


— 10 


— 10 


—40 


— 10 


60 




155 


27 


8.0 





20 





— 10 


— 10 






156 


32 


8-5 


— 20 


— 10 


70 


— 20 


30 






157 


35 


8.2 


5o 


— 10 


—30 








—60 




158 


39 


7-8 


20 


40 


10 


20 


— 20 


— 10 


—20 






Section I — Final mental 


age 9 years 






159 


8 


7-6 


20 


20 


60 


60 








160 


9 


7.0 


50 


10 


40 


30 


60 


20 


10 


161 


9 


7.1 


30 


30 


30 


20 


80 






162 


9 


8.2 


30 


50 


30 










163 


9 


8.4 


SO 


30 


— 10 










164 


10 


9-3 


20 


40 


— 10 










165 


11 


9.1 


10 





5o 


10 


—40 






166 


12 


8.4 


10 


20 


50 


20 


30 






167 


13 


7-5 


50 


60 


30 





20 






168 


13 


8.6 


10 


60 


30 


20 








169 


13 


8.9 


40 


20 


30 











170 


14 


8.4 


40 


50 


20 










171 


14 


8.4 


30 


60 


30 


— 20 


— 20 






172 


15 


8.6 


10 





10 


10 


20 


20 




173 


17 


91 


— 20 


50 


40 










174 


17 


9-3 


20 


—50 













175 


18 


9-5 


— 20 


60 


—70 











176 


19 


9.0 








20 










177 


21 


8.8 


10 


10 


20 












178 


23 


8.9 


40 


— 20 


10 


30 


20 






179 


26 


9.4 





— 20 





30 


— 10 


— 20 




180 


28 


9-1 


30 


60 


— 10 










181 


30 


9.0 


20 





20 





— 10 






182 


30 


9.6 





20 


30 





—30 






183 


33 


9-4 


10 


10 


10 


10 


10 






184 


40 


9-3 


10 








10 


20 










Section 


J — Final mental 


age 10 


years 






185 


11 


8.0 


40 


40 


50 


30 


40 






186 


11 


8-5 


40 


30 


80 










187 


14 


10.4 





20 


10 


10 








188 


16 


9-3 


20 


40 


—40 


— 20 


00 


10 


— 20 


189 


16 


9-9 


50 





30 


10 


—40 





30 



30 



58 EDGAR A. DOLL 

Table 3 (continued) 
Section J — Final mental age 10 years (continued) 





First 


First 




Successive rates of 


me: 


Subject 


life 


mental 


I St 


2nd 


3rd 


4th 


5th 


No. 


age 


age 


year 


year 


year 


year 


yeai 


190 


16 


10.5 


—40 


10 


20 






191 


16 


10.7 


20 


20 


10 


—40 





192 


17 


10.8 


10 


30 


10 


—30 




193 


18 


9.8 


30 


— 10 


— 10 


20 


10 


194 


19 


9.4 


40 


70 


30 





20 


195 


20 


9-9 


20 


30 


— 20 


10 


30 


196 


22 


1 0.0 


10 








— 10 ■ 


—10 


197 


22 


10.7 


—30 





10 


10 





198 


24 


10.2 





20 





• 


—10 


199 


24 


10.2 


30 


— 20 





20 


30 


200 


25 


10.6 





20 


30 






201 


28 


9.8 


40 


20 





■ 


—10 


202 


44 


10.5 


— 20 





5o 






203 


46 


9.6 


30 


30 


20 


— 10 






6th 7th 8th 
year year year 



-SO 
40 



3. Only 38 subjects gain as much as at least one year within 
at least five years. All but one are under 15 years of age at 
the first record. None of these increases as much as a year after 
15 years. Ninety-five subjects are under 15 years of age at the 
first record; hence only 39 per cent of these subjects who are 
under 15 at first record show improvement amounting to at least 
one year in 5 years. That is, 61 per cent of subjects (58 cases) 
who are under 15 years of age at first record fail to show mental 
age increases amounting to as much as a single year after in 
most cases 4 or 5 years. 

The distribution of 'gains' and 'no gains' for all subjects under 
15 years of age at first record by final mental level is given in 
Table 4. The last line of Table 4 is a clear indication of the 

Table 4 

Relation of improvability to final mental level among subjects 
under 15 years of life age. 
Final mental age 123 45 6789 10 Tot. 

Number subjects each mental age 5 7 5 8 6 8 27 13 13 3 95 
Number gaining one year or more 1 2 4 14 5 9 2 37 

Per cent gaining a year or more o o o 13 33 50 52 39 69 67 39 

general dependence of age of arrest upon level of arrest. The 
percentage of subjects under 15 years of age at first record who 
increase as much as at least one year in at least 5 years steadily 
increases from o at final mental age 1 year to 67 at final mental 
age 10 years. Or, conversely, the number of those who fail to 



THE GROWTH OF INTELLIGENCE 59 

increase becomes steadily less and less from the lower to the 
higher mental levels. That is to say, the lower the mental level 
the greater the number of subjects who have reached their final 
level. And since the distribution of first life ages is approxim- 
ately the same for all the mental levels (see Table 2) it follows 
that the lower the mental level the earlier the age of arrest. 

4. It is extremely difficult to fix the actual age of arrest for 
each mental level from the data in hand, because of the lack of 
sufficient numbers of young subjects. We have observed that 
all subjects regardless of specific mental level are arrested be- 
fore 15 years of age, in the sense that after 14 they do not show 
as much as one year of mental age increase. We can go further. 
The ages for each mental level at which all subjects are arrested 
are as follows : 

Mental age level 123456789 10 
Age of arrest 10 8 6 11 12 15 15 12 15 14 

This table is irregular because of inadequate data. All subjects 
were arrested at least by these ages. The majority of the sub- 
jects (166 subjects, or 82 per cent) do not improve materially 
after the first recorded age. Fifty-eight of these are under the 
age of 15, yet they were fully arrested when first examined. 
That individual variability is influenced by both age and mental 
age is obvious from careful inspection of Table 2. The idiots 
(mental age 1 and 2 years) are all arrested by 10 years of age, 
but we cannot say how much sooner. At mental age 3 years all 
subjects are arrested by 6 years of age, but there are only a few 
young subjects. At mental age 4 there is only one subject under 
age 11. And so> on for the other levels. 

5. There is observed among subjects who are older than the 
age of arrest for their mental level a slight tendency to decrease 
in successive examinations independently of actual age. This is 
strong evidence that there is not only no marked influence of 
coaching but that if the factor of age or experience plays a posi- 
tive part on some tests it also must play a negative part on others. 
That is, if some tests are tests of age rather than tests of intelli- 
gence, increase of age may bring about more losses than gains. 
Probably, however, the institution life tends to shear the subjects 



60 EDGAR A. DOLL 

of certain superficial appearances of intelligence of the sort 
which might give a spuriously high mental age at first examina- 
tions. That is, the so-called tests of information like naming 
days of the weeks, giving the date, and the like might be passed 
on admission but not passed after several years in the institu- 
tional environment. But in any case the losses are very slight 
and so irregular from subject to subject that the question is not 
a practically serious one. 

6. In general the data lead to four general principles, none of 
which can be stated with statistical exactness because of inade- 
quate data; (a) age of arrest is associated with level of arrest, 
although the numerical relationship cannot yet be stated (cf. 
however, pp. 73 to 76) ; (b) within a particular final mental age 
group the younger subjects are more likely to improve than the 
older, independently of actual retardation; (c) gains are re- 
stricted to subjects who are under 15 years of age; and (d) 
variability is very great and prognosis on the basis of mental 
age alone practically impossible for individuals. That is, initial 
mental age gives no definite indication of final mental age. The 
actual course of mental age growth must be traced out by actual 
repeated examinations in the case of feeble-minded subjects. 

An objection may be raised against the method of analysis on the ground 
that in using one year of mental age increase as a minimum indication of 
significant increase we have employed a misleading criterion. A year of 
difference in mental age does not mean the same thing at different life ages 
(cf. pp. 85 ff.). Moreover, a year of increase at mental age 2 years is an 
increase of 50 per cent of mental age while at mental age 10 years it is an 
increase of only 10 per cent. We may meet this objection by certain prac- 
tical considerations. It is impracticable to recognize increases of less than 
one year because of what Goddard calls 'the normal variability of the ab- 
normal mind' ; unless the increases are consistent in trend they ordinarily 
represent only minor fluctuations in the mental level. We need not, how- 
ever, insist upon this point. We shall come to similar but more exact con- 
clusions by a method of analysis which is independent of this criterion and 
employs instead the actual average mental age increments from age to age 
for each mental age group. 

Rate of development. — The second phase of the problem of 
feeble-minded growth calls for an examination of the annual 
rate of growth. The data have already been treated in such a 
way as to show the annual rates of mental age increase (cf. 



THE GROWTH OF INTELLIGENCE 61 

Table 3) in terms of a percentage of the average normal rate 
(which by the Binet Scale is standardized at one year of increase 
in mental age for each year of increase in life age). The analy- 
sis of Table 2 and Table 3 has already shown that growth is 
limited to the subjects who are under 15 years of age. We may 
therefore confine the study of rate of growth to subjects under 
15 years of age. 

Most of the subjects under 15 years of age are developing at 
a very slow rate. We have seen that only 37 of them, or 39 per 
cent, have gained as much as a year or more after 3 to 5 years 
of repeated examining. That is, 61 per cent gain less than 1 
year in 3 to 5 years or gain at a net average rate which is never 
greater than 30 per cent of the average normal rate and ordi- 
narily is less than 20 per cent. Even among those who do gain 
a year this gain frequently requires 5 years of time, which is a 
net average rate of only 20 per cent. 

Rate of growth may be a function of life age, or of mental 
age, or of degree of retardation. (It is of course affected by 
physiological conditions due to accident, disease, or hereditary 
predisposition but in the present discussion we are obliged to 
ignore these influences.) Our study of individual subjects (cf. 
Tables 2 and 3) has indicated that individual variations in rate 
are very great. Some subjects make no significant gains even 
when age, mental age and degree of retardation all suggest ex- 
pectation of gains. On the other hand some subjects whose 
mental ages are low, whose life ages are high and whose re- 
tardation is very great, suddenly show marked increases in 
mental growth. 

We must therefore resort to a study of averages, and we must 
study the data without making assumptions which might limit 
the value of the conclusions. Hence we must study the influ- 
ences of age and mental age independently before we can study 
the influence of degree of retardation, which is the relation of 
mental age to life age. We cannot, therefore, employ such a 
device as the intelligence quotient, because that device is founded 
on assumptions whose validity we desire to test. This necessity 
makes statistical treatment of the data very difficult. A study of 



62 EDGAR A. DOLL 

the influence of age gives obscure results because of the unequal 
distributions of mental age at each life age grouping. Similarly 
a study of the dependence of rate upon mental age is spuriously 
affected by unequal distributions of life age at each mental age 
grouping. The desirable statistical method would be to calcu- 
late the coefficients of correlation and then correct for constric- 
tion or dilation caused by 'spurious' factors. This method is of 
doubtful significance because of the striking deviations of indi- 
vidual subjects, the small numbers of subjects in some catego- 
ries, and the variable factors in the selection of subjects. More- 
over, the relationship between rate and life age is non-rectilinear, 
while the relationship between rate and mental age is rectilinear. 
But the greatest difficulty is that of selecting a satisfactory basis 
of classification. 

Trial calculations indicate that the rate of growth is practical- 
ly independent of mental age. There is a slight negative corre- 
lation between rate of growth and mental age. But this is due 
to a negative correlation between rate and life age between 8 and 
15 years of age, combined with a slight positive correlation be- 
tween mental age and life age. 

Relation of rate to life age.- — We are concerned with the 
amounts of increase as well as the strength of the tendency. 
Therefore it seemed advisable to calculate the actual average 
rates of increase for the successive life ages. We could then 
plot the average functional relation between rate and life age. 
If there were at any life age a correlation between rate and 
mental age it would be necessary to allow for this influence. But 
if the distribution of mental ages at each life age period is ap- 
proximately the same from age to age, then an average rate of 
growth by life age may be established independently of mental 
age. Or if there is no significant correlation between mental age 
and rate of growth at each life age grouping, then again the rate 
of growth will appear as a function of life age independently 
of mental age. 

Table 5 is presented to show the annual growth increments by 
life age. This tabulation covers only the crucial period, namely 
the ages below 16 years at first record. The data of Table 5 



THE GROWTH OF INTELLIGENCE 



63 





Relation 


of annual rate 








age, men 


Section 


A— Life 


age 


7 years 




7 subjects 




Subject '. 


Mental 


1. Q. 


Annual 


No. 


age 




rate 


15 


2-5 


36 


40 


16 


3-6 


51 





44 


3-7 


S3 


10 


86 


4.9 


70 


no 


87 


5-6 


80 


40 


88 


5-7 


81 


no 


89 


5-7 


81 


80 


Ave. 


4-5 


65 


56 


Section 


B—Life 


age 


8 years 




22 subji 


;cts 




9 


2.0 


25 





8 


2.7 


34 


20 


15 


2.9 


36 


40 


7 


3-1 


39 


70 


28 


3-3 


4i 


90 


16 


3-6 


45 


40 


44 


3-8 


48 


10 


61 


3.8 


48 


40 


62 


4.0 


50 


30 


90 


4-4 


55 


no 


91 


4-5 


56 


100 


92 


5-5 


69 


20 


93 


5-9 


74 


80 


86 


6.0 


75 


40 


87 


6.0 


75 


30 


94 


6.3 


79 


50 


89 


6.5 


81 


30 


132 


6.6 


83 


60 


88 


6.8 


85 


30 


133 


7.0 


88 


20 


134 


7-3 


9i 


80 


159 


7-6 


95 


20 


Ave. 


5-0 


62 


46 


Section C — Life 


age 9 years 




34 subjects 




10 


1.8 


20 


10 


9 


2.0 


22 





8 


2.9 


32 


20 


17 


3-4 


38 





45 


3-6 


40 


100 


7 


3-8 


42 


— 10 


44 


3-9 


43 


20 


16 


4.0 


44 


— 20 


28 


4.2 


47 


20 


61 


4.2 


47 


90 


62 


4-3 


48 


80 


95 


4-3 


48 


70 



Table 5 

: of mental age increase 

tal age, and I. Q. 



to life 



Section C — (continued) 



Subject 


Mental 


I. Q. 


Annual 


No. 


age 




rate 


63 


4-5 


50 


80 


90 


5-5 


61 


70 


9i 


5-5 


61 


50 


92 


5-7 


63 


60 


87 


6.3 


70 


40 


86 


6.4 


7i 


50 


96 


6.6 


73 





93 


6.7 


74 


40 


97 


6.7 


74 


60 


89 


6.8 


76 


20 


94 


6.8 


76 


30 


135 


7.0 


78 


10 


160 


7.0 


78 


50 


88 


7-i 


79 


40 


161 


7-1 


79 


30 


132 


7-2 


80 


40 


133 


7-2 


80 


20 


136 


7.2 


80 


30 


159 


7-8 


87 


20 


134 


8.1 


90 


10 


162 


8.2 


91 


30 


163 


8.4 


93 


50 


Ave. 


5-7 


63 


36 


Section D — Life 


age 10 


years 




41 subjects 




1 


i-7 


17 





10 


1.9 


19 


20 


9 


2.0 


20 





8 


3-i 


3i 


—40 


17 


3-4 


34 


10 


7 


3-7 


37 


—40 


44 


4.1 


41 


80 


28 


4.4 


44 





45 


4.6 


46 


60 


95 


5-0 


50 


80 


61 


5-i 


51 


40 


62 


5-i 


51 


20 


63 


5-3 


53 


70 


9i 


6.0 


60 


70 


64 


6.2 


62 


10 


90 


6.2 


62 


40 


92 


6-3 


63 


30 


96 


6.6 


66 


10 


87 


6.7 


67 


10 


86 


6.9 


69 





&9 


7.0 


70 


40 


98 


7.0 


70 


10 


93 


7-1 


7i 


— 10 


94 


7-i 


7i 


40 



6 4 






EDGAR 
Table 5 


A. DOLL 
(continued) 








Section D — (continued) 


Section E — (continued) 


Subject 


Mental 


1. Q. 


Annual 


Subject 


Mental 


I. Q. 


Annual 


No. 


age 




rate 


No. 


age 




rate 


135 


7-1 


71 


30 


99 


7-1 


65 





137 


7-1 


71 


50 


102 


7-2 


65 


10 


97 


7-3 


73 


10 


89 


7-4 


67 


10 


99 


7-3 


73 


— 20 


97 


7-4 


67 


— 10 


161 


7-4 


74 


30 


135 


7-4 


67 


30 


133 


7-4 


74 


20 


94 


7-5 


68 


20 


88 


7-5 


75 


10 


137 


7-6 


69 


20 


136 


7-5 


75 


20 


88 


7-6 


69 


— 10 


160 


7-5 


75 


10 


133 


7-6 


69 


10 


132 


7.6 


76 


30 


160 


7-6 


69 


40 


138 


7-6 


76 


80 


136 


7-7 


70 


20 


139 


7-8 


78 


60 


161 


7-7 


70 


30 


159 


8.0 


80 


60 


132 


79 


72 


10 


134 


8.2 


82 





185 


8.0 


73 


40 


162 


8.5 


85 


50 


134 


8.2 


75 


— 20 


163 


8.9 


89 


30 


138 


8.4 


76 


10 


164 


9-3 


93 


20 


139 


8.4 


76 


10 










186 


8.5 


77 


40 


Ave. 


6.2 


62 


25 


159 


8.6 


78 


60 










162 


9.0 


82 


30 


Section E — Life 


age 11 


years 


165 


91 


83 


10 




54 subj 


ects 




163 


9-2 


84 


— 10 


1 


1-7 


15 


20 


164 


9-5 


86 


40 


9 


2.0 


18 













10 


2.1 


19 


10 


Ave. 


6.3 


57 


21 


12 


2.2 


20 


20 










8 


2.7 


25 


— 20 


Section F — Life 


age 12 


years 


11 


2.8 


25 


20 




58 subj 


ects 




7 


3-3 


30 


—40 


Subject 


Mental 


1. Q. 


Annual 


17 


3-5 


32 





No. 


age 




rate 


29 


3-6 


33 


30 


2 


J-3 


11 


10 


18 


4-3 


39 


20 


1 


1.9 


16 


10 


30 


4-3 


39 


20 


10 


2.2 


18 


— 10 


28 


44 


40 


— 10 


12 


2.4 


20 





44 


4.9 


45 


50 


8 


2.5 


21 


10 


45 


5-2 


47 


70 


7 


2.9 


24 


—30 


62 


5-3 


48 


20 


11 


3-0 


25 


— 10 


61 


5-5 


50 


40 


19 


3-0 


25 


20 


95 


5-8 


53 


90 


17 


3-5 


29 





65 


5-9 


54 


40 


29 


3-9 


33 


10 


100 


5-9 


54 


60 


3i 


3-9 


33 


10 


63 


6.0 


55 


10 


28 


43 


36 


20 


64 


6.3 


57 


10 


46 


43 


36 


20 


66 


6.4 


58 


50 


32 


4-4 


37 





90 


6.6 


60 


90 


18 


4-5 


38 


— 10 


92 


6.6 


60 


50 


30 


45 


38 


— 20 


9i 


6.7 


61 


20 


47 


45 


38 


20 


96 


6.7 


61 





33 


47 


39 


10 


87 


6.8 


62 


20 


67 


5-1 


43 


90 


86 


6.9 


63 





44 


54 


45 


20 


93 


7.0 


64 


20 


62 


5-5 


46 


30 


101 


7.o 


64 


10 


48 


5-6 


47 


20 


98 


7-i 


65 


10 


45 


5-9 


49 






THE GROWTH OF INTELLIGENCE 



65 



Table 5 (continued) 



Section F — (continued) 
Subject Mental I. Q. Annual 



No. 


age 




rate 


61 


5-9 


49 


20 


63 


6.1 


51 


—40 


65 


6.3 


53 





64 


6.4 


53 


20 


100 


6-5 


54 


10 


95 


6.7 


56 


40 


96 


6.7 


56 


20 


66 


6.9 


58 


20 


86 


6-9 


58 


40 


9i 


6-9 


58 


10 


103 


6.9 


58 


60 


87 


7.0 


58 


30 


92 


7-i 


59 


40 


101 


7-1 


59 





99 


7-i 


59 


30 


93 


7.2 


60 


10 


98 


7.2 


60 


10 


97 


7-3 


61 


40 


102 


73 


61 


40 


90 


7-5 


63 





94 


7-7 


64 


— 20 


133 


7-7 


64 


40 


135 


7-7 


64 


30 


137 


7-8 


65 


30 


137 


7-9 


66 


10 


134 


8.0 


67 


10 


160 


8.0 


67 


30 


161 


8.0 


67 


20 


166 


8.4 


70 


10 


185 


8.4 


70 


40 


138 


8.5 


7i 


10 


139 


8-5 


7i 





186 


8.9 


74 


30 


165 


9.2 


77 





164 


9-9 


83 


— 10 



Ave. 



6.0 



SO 



15 



Section G — Life age 13 years 
64 subjects 



3 


1.0 


8 





2 


1.4 


11 


10 


4 


1.7 


13 


20 


1 


2.0 


15 


— 10 


13 


2.0 


15 





10 


2.1 


16 


—30 


12 


2.4 


18 





8 


2.6 


20 


40 


11 


2.9 


22 


— 20 


19 


3-2 


25 


40 


17 


3-5 


27 





29 


4.0 


31 


— 20 


31 


4.0 


31 


30 



Section G — (continued) 
Subject Mental I. Q. Annual 



No. 


age 




rate 


30 


4-3 


33 


10 


18 


4.4 


34 


—10 


32 


4-4 


34 


— 20 


28 


4-5 


35 


30 


46 


4-5 


35 


20 


47 


4-7 


36 


10 


33 


4.8 


37 


— 20 


49 


5-1 


39 





68 


5-2 


40 


60 


44 


5-6 


43 


10 


63 


5-7 


44 


30 


48 


5-8 


45 


10 


62 


5-8 


45 


20 


67 


6.0 


46 


50 


104 


6.0 


46 


70 


61 


6.1 


47 


10 


65 


6-3 


48 





105 


6.4 


49 


50 


106 


6.5 


50 


20 


64 


6.6 


5i 


10 


100 


6.6 


5i 


60 


107 


6.6 


5i 


30 


96 


6.9 


53 


50 


91 


7.0 


54 





66 


7.1 


55 





95 


7.1 


55 


20 


101 


7-i 


55 





98 


7-3 


56 


20 


108 


7-3 


56 


20 


90 


7-5 


58 


10 


94 


7-5 


58 


20 


103 


7-5 


58 


10 


167 


7-5 


58 


50 


97 


7-7 


59 


20 


102 


7-7 


59 


20 


109 


7-8 


60 


50 


140 


7-9 


61 


20 


135 


8.0 


62 


20 


133 


8.1 


62 


40 


134 


8.1 


62 


10 


137 


8.1 


62 


20 


161 


8.2 


63 


80 


160 


8.3 


64 


60 


139 


8.5 


65 


20 


166 


8-5 


65 


20 


138 


8.6 


66 





168 


8.6 


66 


10 


185 


8.8 


68 


50 


169 


8.9 


69 


40 


165 


9.2 


7i 


50 


186 


9.2 


7i 


80 



Ave. 



6.0 



46 



21 



66 



EDGAR A. DOLL 



Table 5 (continued) 



Section H — Li: 


Ee age 14 years 




63 su 


bjects 




Subject 


Mental 


I. Q. 


Annual 


No. 


age 




rate 


3 


1.0 


7 





5 


1.4 


10 


—40 


2 


1-5 


n 


10 


1 


1.9 


14 


— 10 


4 


1.9 


14 


10 


13 


2.0 


14 





12 


2.4 


17 





11 


2.7 


19 


10 


19 


3-6 


26 


— 20 


29 


3-8 


27 





34 


3-8 


27 


30 


35 


3-9 


28 


40 


32 


4.2 


30 


—30 


18 


4-3 


3i 


— 60 


31 


4-3 


3i 


— 10 


33 


4.6 


33 


30 


46 


4-7 


34 


10 


47 


4.8 


34 


20 


49 


5-1 


36 


— 10 


68 


5-8 


4i 


10 


48 


5-9 


42 





62 


6.0 


43 


20 


63 


6.0 


43 


10 


65 


6-3 


45 


—30 


67 


6.5 


46 


— 10 


64 


6.7 


48 


20 


104 


6.7 


48 


40 


106 


6.7 


48 


20 


in 


6.7 


48 


50 


105 


6-9 


49 


— 10 


107 


6.9 


49 


20 


no 


6.9 


49 


40 


91 


7.0 


50 


10 


66 


7-i 


5i 


10 


101 


7-i 


5i 





100 


7.2 


5i 


30 


95 


7-3 


52 





96 


7-4 


53 


20 


98 


7-5 


54 





108 


7-5 


54 


— 10 


112 


7-5 


54 





103 


7-6 


54 





102 


7-9 


56 


— 20 


141 


8.0 


57 





167 


8.0 


57 


60 


140 


8.1 


58 





142 


8.1 


58 





134 


8.2 


59 





135 


8.2 


59 


—30 


143 


8.2 


59 


20 


109 


8-3 


59 





137 


8-3 


59 


30 



Subject H — (continued) 
Subject Mental I. Q. Annual 



No. 


age 




rate 


170 


8.4 


60 


40 


171 


8.4 


60 


30 


144 


8.5 


61 





138 


8.6 


61 


20 


166 


8.7 


62 


50 


168 


8.7 


62 


60 


160 


8-9 


64 


20 


169 


9-3 


66 


20 


185 


9-3 


66 


30 


165 


9-7 


69 


10 


187 


10.4 


74 





Ave. 


6.3 


45 


9 


Section I — Life 


age 1 


5 years 




63 subjects 




Subject 


Mental 


I. Q. 


Annual 


No. 


age 




rate 


3 


1.0 


7 





5 


1.0 


7 


20 


4 


2.0 


13 





13 


2.0 


13 


— 10 


n 


2.8 


19 


10 


20 


2.8 


19 





21 


3-2 


21 


— 20 


19 


34 


23 





18 


3-7 


25 


— 10 


29 


3-8 


25 


20 


34 


4.1 


27 


10 


31 


4.2 


28 


— 10 


35 


4-3 


29 


— 10 


36 


4-5 


30 


20 


46 


4.8 


32 


20 


33 


4.9 


33 





47 


5-0 


33 


10 


49 


5-0 


33 


— IO 


48 


5-9 


39 





68 


5-9 


39 


— 20 


63 


6.1 


4i 


10 


69 


6.3 


42 


20 


67 


6.4 


43 


30 


70 


6.4 


43 


30 


7i 


6.4 


43 


10 


72 


6.7 


45 


— 10 


105 


6.8 


45 





106 


6.9 


46 


10 


9i 


7-i 


47 


20 


101 


7-i 


47 





104 


7.1 


47 





107 


7-i 


47 


20 


66 


7.2 


48 


— 20 


in 


7.2 


48 


— 10 


113 


7.2 


48 






THE GROWTH OF INTELLIGENCE 67 

Table 5 (continued) 



Section I— 


(continued) 


Section I — 


(continued) 


Subject 


Mental 


I. Q. 


Annual 


Subject 


Mental 


I. Q. 


Annual 


No. 


age 




rate 


No. 


age 




rate 


95 


7-3 


49 





145 . 


8.5 


57 


20 


no 


7-3 


49 


10 


137 


8.6 


57 


10 


108 


7-4 


49 


40 


167 


8.6 


57 


30 


98 


7-5 


50 


— 20 


172 


8.6 


57 


10 


100 


7-5 


So 





171 


8.7 


58 


60 


112 


7-5 


50 





170 


8.8 


59 


50 


102 


7-7 


5i 


— 10 


160 


9.1 


61 


10 


146 


7-7 


5i 





166 


9.2 


61 


20 


135 


7-9 


53 


30 


168 


9-3 


62 


30 


141 


8.0 


53 


10 


169 


9-5 


63 


30 


140 


8.1 


54 





185 


9.6 


64 


40 


142 


8.1 


54 


20 


165 


9-8 


65 


—40 


109 


8-3 


55 





187 


10.4 


69 


20 


143 


8.4 


56 


— 10 










144 


8.5 


57 


— 20 


Ave. 


6.5 


44 


8 



are derived directly from Table 2. The table shows each sub- 
ject at each of his life ages. In the first column is the identifi- 
cation number of each subject corresponding to his position in 
Table 2. The mental age at each life age (that is, the initial 
mental age plus the intervening increment) is given in the second 
column, then the I. Q., or the predicted rate that would ensue 
if this ratio (I. Q.) were a constant, then the actual rate of 
growth for the ensuing year. 

It is fairly obvious from this table that there is no consistent 
dependence of rate of growth upon mental age at any life-age 
grouping. Each grouping is arranged in order of ascending 
mental age. But the rate of growth shows no corresponding 
increase in value. As a general rule there is some tendency for 
an increase from the low mental ages to the middle mental ages 
and then a decrease. This is in spite of the fact that the higher 
mental ages show lesser degrees of retardation. The actual 
Pearson coefficients of correlation were computed for age-groups 
9 years and 1 1 years as samples. In each case the coefficient was 
r = .12 (P. E. = .10 and .09 respectively). This is practically 
no correlation, or only as great as might be expected by chance. 
The average rates of increase for each age-group (including also 
some ages above 15) are shown in Table 6. 

Tables 5 and 6 show more clearly than was apparent from 
Table 3 that the average rate of mental age increase is relatively 



68 EDGAR A. DOLL 

Table 6 
Average annual rates of mental age increase by life ages. 





No. of 


Average 


Average 


Average 


Life age 


subjects 


mental age 


I. Q- 


annual rate 


7 


7 


4-5 


65 


56 


8 


22 


5-o 


62 


46 


9 


34 


5-7 


63 


36 


10 


41 


6.2 


62 


25 


ii 


54 


6.3 


57 


21 


12 


58 


6.0 


50 


15 


13 


64 


6.0 


46 


21 


14 


63 


6.3 


45 


9 


IS 


63 


6.5 


44 


8 


16 


57 


6.6 


41 


7 


17 


5i 


6.8 


43 


5 


18 


46 


71 


44 


3 


19 


4i 


7-3 


46 


7 


20 


40 


7-3 


46 


4 


21 


34 


7-3 


46 


9 


22 


32 


7-6 


48 


6 



independent of mental age or degree of retardation. It is in- 
stead a function of life age. There is some tendency at each age 
for the rate to increase with mental age from mental age 1 year 
to about mental age 5 years or 6 years ; after this point the rate 
tends to decrease. The net result of these compensating tenden- 
cies is to produce a negligible correlation between rate and mental 
age at each life age. Table 6 shows some tendency for the aver- 
age mental ages of each life age group to increase. This is be- 
cause more high-grade subjects are included in the higher age- 
groups. It is generally believed that the high-grade and less re- 
tarded subjects have higher rates of development than the low- 
grade and grossly retarded subjects. We should therefore ex- 
pect that the entry of high-grade subjects would increase the 
rate; but as a matter of fact the rate decreases with increase of 
life age in spite of the entry of the high-grade subjects. With- 
out them it might decrease more rapidly or come to a mini- 
mum at an earlier age than is shown in Table 6. 

We may conclude from Tables 5 and 6 that the average rate 
;, of mental age increase of these feeble-minded subjects decreases 
regularly and steadily between the ages of 8 and 14 years and 
reaches a practical minimum at 15 or 14 years. This is in spite 
of the fact that in the higher age groups we have an increasingly 
greater number of high-grade and less retarded subjects. It is 



THE GROWTH OF INTELLIGENCE 69 

probably something more than a coincidence that this age of 
arrest of the average rate of growth coincides with the age of 
arrest of average normal subjects previously discussed. 

This conclusion that the average rate of growth decreases with 
increase of life age seems to contradict one of our previous con- 
clusions that the age of arrest is a function of the level of ar- 
rest. It is therefore desirable to study the data from still an- 
other point of view. 

Rate of growth of 'improving 3 subjects. — The treatment of 
data offered in Table 5 is open to the criticism that a majority 
of the subjects have a rate of increase which is practically negli- 
gible. It has been shown (cf. Tables 2 and 3) that 61 per cent 
of all subjects under 15 years of age at first examinations do not 
improve as much as a year mentally in 3 to> 5 years; for these 
subjects the rate of increase represents only minor fluctuations 
plus or minus from a final mental age level. In other words 61 
per cent of the subjects represented in Table 5 are not increasing 
significantly in mental age. The inclusion of these subjects has 
a tendency to obscure the actual influence of mental age upon 
rate of increase, that is to say, they contribute negatively to the 
results summarized in Table 6. Consequently it is desirable to 
study only the 'improving' subjects who contribute positively to 
the rate of increase. These cases, who constitute 39 per cent of 
all subjects under 15 years of age at first examinations, have 
been gathered together for special study. They have been se- 
lected from Table 2 (as indicated by the subject numbers) on 
the basis of having gained at least a year of mental age in 3 
to 5 years of life age. The successive net total mental age in- 
creases of these subjects at each year of repeated examination 
are presented in Table 7, arranged in ascending order of life- 
age at first record. 

We might measure the strength of the tendency of rate to be 
associated with age or mental age by means of correlation coeffi- 
cients. But as was previously pointed out this would yield only a 
measure of correlation tendency. Moreover, there are certain 
spurious influences which cannot fully be allowed for. 10 To 
10 The limitations of the correlation method have been well stated by 



70 EDGAR A. DOLL 

make an analysis which shall show the actual amounts of in- 
crease in rate with increase in age and at the same time show 
the influence of mental age and the influence of repeated testing 
we have sorted out from Table 7 the subjects whose first ages 
are 7, 8 and 9 years for special study, these ages representing a 
majority of the subjects of Table 7. Fearing a possible in- 
fluence of repeated examination, as a result of which the suc- 
cessive increases might show gains due to practice or experience 
in the tests, we have not combined all subjects at a given age 
(as was done in Table 5) but have grouped the subjects only 
according to first life ages. The treatment of these subjects is 
presented in Table 8. This table shows the successive ages, the 
mental ages for each age, the I. Q.'s and the rates of growth of 
those improving subjects whose first life ages were 7, 8 and 9 
years. Unfortunately the number of subjects is rather small at 
each age. 

Inspection shows that there is no positive correlation between 
increase in rate and increase in mental age or I. Q. Indeed there 
is an observable tendency for a negative correlation, that is, a 
tendency for the lower mental ages or the more retarded sub- 
jects to show larger rates of increase than the higher mental 

Thurstone (33, p. 3). He says: "A correlation coefficient considerably less 
than unity may be explained in at least four different ways: (1) the obser- 
vations may be so inaccurate as to obscure the relationship; (2) the two 
variables may be related through a common third variable which, if not 
controlled or kept constant, plays havoc with the experiment; (3) the re- 
gression may be non-linear, in which case the Pearson coefficient, r, is almost 
meaningless ; (4) the two variables may be intrinsically independent." It 
seemed desirable to measure the numerical degree of relationship between 
rate of growth and mental age by means of the correlation coefficient. But 
this correlation is affected by the relation of these two variables to the factor 
of life age. Two of the regressions proved to be linear and one non- 
linear, an added difficulty which would render the original correlation not 
significant, since the correction could not be made for the third variable 
under such conditions. Similarly, the correlation between rate of growth 
and life age (non-linear regression) is influenced by the correlation be- 
tween rate and mental age (linear regression) and the influence of the 
last-mentioned variable cannot be allowed for by available statistical meas- 
ures. (I am indebted to Prof. Truman Lee Kelly for an authoritative opin- 
ion on this point.) 



THE GROWTH OF INTELLIGENCE 



7* 











Table 7 
















Mental 


age increases 


of 'improving' subjects. 








First 


First 




Net total 


mental age 


increases 




Subject 


life 


mental 


after 


after 


after 


after 


after 


after 


after 


after 


No. 


age 


age 


1 yr. 


2 yrs. 


3 yrs. 


4 yrs. 


5 yrs. 


6 yrs. 


7 yrs. 


8 yrs 


44 


7 


3-7 


.1 


.2 


•4 


1.2 


i-7 


1-9 


2.0 


2.0 


86 


7 


4-9 


1.1 


i-5 


2.0 


2.0 


2.0 


2.4 






87 


7 


5-6 


•4 


•7 


i.i 


1.2 


1.4 


1-7 






88 


7 


5-7 


i.i 


1.4 


1.8 


1.9 


1.8 








89 


7 


5-7 


.8 


i.i 


1.3 


1.7 


1.8 








28 


8 


3-3 


•9 


i.i 


i.i 


1.0 


1.2 


i-5 






61 


8 


3-8 


•4 


1-3 


i-7 


2.1 


2.3 


2.4 






62 


8 


4.0 


•3 


i.i 


1.3 


1-5 


1.8 


2.0 


2.2 




90 


8 


4-4 


i.i 


1.8 


2.2 


3-i 


3-i 


3-2 






9i 


8 


45 


1.0 


1-5 


2.2 


2.4 


2-5 


2.5 


2.6 


2.8 


92 


8 


5-5 


.2 


.8 


i.i 


1.6 


2.0 








93 


8 


5-9 


.8 


1.2 


i.i 


i-3 


1.4 








94 


8 


6.3 


•5 


.8 


1.2 


1.4 


1.2 


1-4 






132 


8 


6.6 


.6 


1.0 


1.3 


1.4 










133 


8 


7.0 


.2 


•4 


.6 


•7 


i.i 


1-5 






159 


8 


7-6 


.2 


•4 


1.0 


1.6 










45 


9 


3-6 


1.0 


1.6 


2.3 


2.3 










63 


9 


4-5 


.8 


1-5 


1.6 


1.2 


i-5 


1.6 


i-7 




95 


9 


4-3 


•7 


i-5 


2.4 


2.8 


30 


3-0 


3-0 


2.8 


97 


9 


6-7 


.6 


•7 


.6 


1.0 


1.2 








135 


9 


7.0 


.1 


•4 


•7 


1.0 


1.2 


•9 


1.2 


1.4 


160 


9 


7.0 


•5 


.6 


1.0 


i-3 


1.9 


2.1 


2.2 




161 


9 


7-1 


•3 


.6 


•9 


i.i 


1.9 








162 


9 


8.2 


•3 


.8 


i.i 












137 


10 


7-i 


•5 


•7 


1.0 


1.2 


i-5 


1.6 


1.4 




138 


10 


7-6 


.8 


•9 


1.0 


1.0 


1.2 








100 


11 


5-9 


.6 


•7 


1.3 


1.6 


1.6 








185 


11 


8.0 


•4 


.8 


1.3 


1.6 


2.0 








186 


11 


8-5 


•4 


•7 


i-5 












67 


12 


5-i 


•9 


1.4 


1-3 


1.6 










166 


12 


8.4 


.1 


•3 


.8 


1.0 


1-3 








104 


13 


6.0 


■7 


i.i 


i.i 


I.I 


i.i 


i.i 


1.0 


•9 


105 


13 


6.4 


•5 


•4 


•4 


1.2 


i-3 








167 


13 


7-5 


•5 


i.i 


1.4 


1.4 


1.6 








168 


13 


8.6 


.1 


•7 


1.0 


1.2 










170 


14 


8.4 


•4 


•9 


i.i 












171 


14 


8.4 


•3 


■9 


1.2 


1.0 


.8 








194 


19 


9.4 


•4 


i.i 


i-4 


1.4 


1.6 


i.i 


•9 





ages or the less retarded subjects. 

The average rates of increase at each life age, independently 
of mental age, are collected into Table 9. This table shows the 
average rate at each successive age for the three groups with 
subjects uncombined and then with subjects of similar ages at 
any examination combined. We may note from this table that : 

1. There is a tendency for the first rates at each age group to 
be somewhat higher than the succeeding rates. That is, the 8- 
year-olds at their first record have a higher average than the 



72 



EDGAR A. DOLL 



When 7 years old 

M.A. I.Q. Rate 

3-7 S3 10 

70 

80 



Table 8 

Relation of rate of mental age increase to life age, mental age, 

and I. Q. among 'improving' subjects. 

Section A — Subjects 7 years old at first record 

When 8 years old When 9 years old When 10 years old 4-Yr. 
M.A. I.Q. Rate 
3-9 43 20 



4.9 
5-6 
5-7 
5-7 



«i 
81 



no 
40 

no 
80 



M.A. I.Q. Rate 
3.8 48 10 

75 
75 
85 
81 



6.0 
6.0 
6.8 

6.5 



40 
30 
30 
30 



Av. S.i 73 7o 



When 8 years old 

3-3 41 90 

3-8 48 40 

4.0 50 30 

44 55 no 

4.5 56 100 

5.5 69 20 
5.9 74 80 
6.3 79 50 

6.6 83 60 
7.0 88 20 
7-6 95 20 

Av. 5.4 67 56 



5-8 73 28 

Section B — Subjects I 
When 9 years old 



6.4 
6.3 
71 
6.8 

6.1 



M.A. I.Q. Rate Ave. 
4.1 41 80 30 



7i 
70 

79 
76 

68 



50 

40 
40 
20 

34 



6.9 
6.7 
7-5 
7.o 



69 
67 
75 
70 



o 
10 
10 

40 



6.4 64 28 



years old at first record 
When 10 years old When n years old 



4.2 
4.2 
4-3 
5-5 
5-5 
5-7 
6.7 
6.8 
7.2 
7.2 
7-8 



47 
47 
48 
61 
61 
63 
74 
76 
80 
80 
87 



5-9 66 



20 
90 
80 
70 
50 
60 
40 
30 
40 
20 
20 

47 



4.4 
5-i 
5-1 
6.2 
6.0 
6.3 
7-i 
7.1 
7-6 
74 
8.0 



44 
51 
5i 
62 
60 
63 
71 
71 
76 

74 
80 



6.4 64 



o 
40 
20 
40 
70 
30 
— 10 
40 
30 
20 
60 

3i 



44 
5-5 
5-3 
6.6 

6.7 
6.6 
7.0 
7-5 
7-9 
7-6 
8.6 



40 
50 

48 
60 
61 
60 
64 
68 
72 
69 
78 



6.7 61 



-10 
40 
20 
90 
20 
50 
20 
20 
10 
10 
60 

30 



Section C — Subjects 9 years old at first record 



When 9 years old When 10 years old When n years old When 12 years old 



50 
30 
48 
43 

40 



25 

52 
38 
78 
60 
40 
33 
35 
35 
18 
40 

41 



3.6 


40 


100 


4.6 


46 


60 


5-2 


47 


70 


5-9 


49 





58 


4-5 


50 


80 


5-3 


53 


70 


6.0 


55 


10 


6.1 


51 


—40 


30 


4-3 


48 


70 


5.o 


50 


80 


5-8 


53 


70 


6.7 


56 


40 


70 


6.7 


74 


60 


7-3 


73 


10 


74 


67 


— 10 


7-3 


61 


40 


25 


7-0 


78 


10 


7-i 


7i 


30 


74 


67 


30 


7-7 


64 


30 


25 


7.0 


78 


50 


7-5 


75 


10 


7-6 


69 


40 


8.0 


67 


30 


28 


7-1 


79 


30 


74 


74 


30 


7-7 


70 


30 


8.0 


67 


20 


23 


8.2 


9i 


30 


8-5 


85 


50 


9.0 


82 


30 


— 


— 


— 





Av. 6.1 67 



5i 



6.6 66 



43 



70 64 36 



7-i 59 17 37 



Table 9 

Average annual rates of mental age increase of 'improving' subjects 

classified by initial life ages. 



First 
age 

7 
8 

9 
Combined 



No. 

5 
n 



24 



Rate 

age 7 

70 



70 



Rate 

age 8 
28 
56 



Rate 
age 9 

34 
47 
51 

42 



Rate 
age 10 

28 
3i 
43 
34 



Rate 

age n 

30 
36 

33 



Rate 4- Year 
age 12 average 
40 
41 
17 37 

17 



7-year-olds at their second record (or when they are 8-year- 
olds). This seems to indicate some influence which tends either 



THE GROWTH OF INTELLIGENCE 73 

to make the first annual rate high or the succeeding rates low, 
over and above the tendency of the rate to decrease as a function 
of age. This may be accounted for as an influence of practice 
or experience on the first re-tests (an influence which steadily 
drops off), or it may be that institutional regime tends either to 
inhibit the full expression of intelligence, by lessening the de- 
mands upon it or by eliminating the exercise of certain intellec- 
tual activities. However, the difference is not great in amount, 
being on the average less than one-tenth of a year. 

2. The combined rates show the same influence of age that was 
shown in Table 6, based on Table 5. The actual averages are 
slightly higher but not so much as might have been expected. 
The fluctuations in rate among the non-improving subjects of 
Table 5 evidently tended to keep the rate up as an average. 

3. The results of this treatment of the data confirm the results 
of the previous mode of treatment in showing that rate of in- 
crease is primarily a function of life age. It does not, however, 
indicate the relation between rate and age of arrest. We there- 
fore proceed to a study of these combined factors. 

Average growth curves of the feeble-minded. — We have now 
demonstrated two marked tendencies in the mental growth of 
the feeble-minded, namely (1) a tendency for the age of arrest 
to be associated with the level of arrest and (2) a tendency for 
the rate of growth to be independent of the mental age. We 
have seen : ( 1 ) that the rate of growth is inconsiderable in the 
low mental ages; (2) that the rate of growth is primarily a 
function of life age; (3) that there is some tendency at each age 
toward a slight negative correlation between rate and degree of 
retardation; and (4) that the high-grade subjects have a lower 
rate of increase than was expected, which is possibly due to their 
relatively higher life ages. 

But the exact form of the average curve of growth is not 
clear from the general arguments presented above. It is desir- 
able, moreover, to observe the connection between rate of 
growth, age of arrest, and level of arrest. The attempt has 
therefore been made to plot the actual average growth curves of 
each final mental age group. This is a difficult undertaking and 



74 



EDGAR A. DOLL 



the results are limited by the small numbers of subjects at some 
ages. Nevertheless, as will be seen, it is possible to obtain fairly- 
smooth growth curves, although it is not possible to determine 
their absolute accuracy because of limitations of the data. 

To accomplish the purpose of plotting the growth curves of 
the several degrees of feeble-mindedness we have attempted to 
determine the average mental age of each final mental age group 
at each of its successive life ages. The computations are based 
on the groupings and data of Table 2. The procedure consists 
in calculating the actual mental ages of each subject at each of 
his life ages. The similar ages of each final mental age group 
are then grouped together and the corresponding mental ages 
are averaged. The detailed tabulations are not presented, but 
the average results are shown in Table 10. This table shows 
for each final-mental-age grouping of subjects the number of 
subjects at each successive life age (for that group) and the 
corresponding average successive mental ages of the group. 
These successive averages constitute the growth curves for each 
final mental age group. The results are clearer when presented 



Life 

age. 

6 

7 
8 

9 
10 
11 
12 
13 
14 
15 
16 

17 
18 



Table 10 
Average developmental progress of each final mental ag 
successive average mental ages at each life 
Final Final Final Final Final Final Final 
M.A. M.A. MA. MA. M.A. MA. M.A. 



1 yr. 
No. Av. 



2 yrs. 3 yrs. 

No. Av. No. Av. 

1 2.6 



4 yrs. 
No. Av. 



5 yrs 
No. Av. 



6 yrs. 7 yrs. 
No. Av. No. Av. 



2.6 
2.6 
2.7 
2.5 
2.5 
2.4 
2.4 
2.4 
2.4 



3-1 
3-3 
3-6 
3-6 
3-9 
3-7 
37 
3-8 
3-3 
3-3 
3-2 
3-2 



3-3 

4.2 

44 
4.1 

4-3 

4.4 



8 4.2 

7 4-i 

7 4-3 

7 4-2 

6 4-3 



3-7 
3.8 
3-8 
4-4 
5-1 
5-i 
5-3 

5-2 

S3 

5-2 



8 5-3 
6 5-4 



4 5-5 

3-9 9 5-8 

4.3 12 6.2 

5.4 14 6.7 
5.9 17 6.9 
6.0 17 7.1 

8 6.1 22 7.2 

8 6.3 21 7.3 
11 6.4 17 7-4 

9 6.4 17 7-3 
8 6.4 15 7.4 
8 6.5 10 74 



e group, 

age. 

Final 

MA. 

8 yrs. 

No. Av. 



3 7-0 

5 7-3 

8 7-5 

8 7-9 

8 8.0 

8 8.2 
11 8.3 
11 8.2 
10 8.3 
10 8.3 

9 8.3 



showing 

Final Final 
MA. M.A. 

9 yrs. 10 yrs. 
No. Av. No. Av. 



7-6 
7.7 
8-3 
8.7 
8.9 
8.6 
8.8 
9.1 
9-3 
9.4 



6 9.4 



2 8.3 
2 8.7 

2 9.0 

3 9-9 
2 10.0 
6 10.2 

6 10.4 

7 10.4 



graphically, but in studying the graph one must not ignore the 
limited numbers of subjects at certain points in the curves. The 
one-subject 'averages' are not represented on the graph. Fig. 



THE GROWTH OF INTELLIGENCE 



75 




76 EDGAR A. DOLL 

10 shows these average growth curves for each final-mental-age 
group. The curves show the average courses of development at 
successive ages up to the final level. 

These growth curves substantiate our previous arguments 
from still another point of view. They also show very clearly 
(subject to limitations of sufficiency of data) the ages of arrest 
and the annual rates of growth. 

We may now determine the average ages of arrest with a 
fair degree of accuracy. The exact determination will depend 
somewhat upon the criterion employed. For practical purposes 
the age of arrest may be taken as the age when (for any curve) 
the growth curve enters the final mental age year-interval. Even 
though the curve may have a slight upward trend after this point 
the net increase is never greater than .5 years. On this criterion 
the ages of arrest may be given as follows : 

Final mental age 123456789 10 
Age of arrest ?? 7 11 11 12 12 12 15 15 

In terms of the grades of feeble-mindedness we may say that 
idiots and low-grade imbeciles are arrested probably before 7 
years of age, upper-grade imbeciles about 12 years, and morons 
about 15 years. 

The average rates of growth are observed to be practically 
negligible for final mental ages 1 year to 4 years inclusive after 
the life age of 6 to 10 years. For final mental age groups 5 to 

9 the growth rates are approximately the same between the life 
ages of 8 and 14 years; the growth curves at these life ages are 
practically parallel (particularly if we were to smooth the ir- 
regularities of the curves for mental ages 6 and 9) and the rates 
are therefore independent of mental age. For final mental age 

10 years the rates of growth for life ages 11 to 15 are about 
the same in amount as those of mental ages 5 to 9 between ages 
8 to 14; that is, the curves of growth are about the same in 
shape but the former is displaced 3 years higher. At all mental 
ages where the subjects are young enough to furnish data for 
the rate of growth the rate is a progressively decreasing variable. 
Moreover, inspection of Fig. 10 lends color to the theory that 



THE GROWTH OF INTELLIGENCE 77 

the upper grades of feeble-mindedness have approximately an 
average normal rate of growth early in life. The higher mental 
age curves of Fig. 10, if projected to the lower ages, would 
branch off from the average normal curve considerably after 
birth, that is, nearly midway in their developmental course. 
Hence there is no prognostic value in mental age (or in degree 
of mental age retardation) in the higher grades of feeble-minded- 
ness prior to about 6 or 8 years of age. The average high- 
grade feeble-minded subject is 'at age' early in life and is only 
potentially feeble-minded from the standpoint of mental age. 
Hence, high-grade feeble-mindedness cannot be diagnosed by 
mental age alone or by a degree of mental age retardation in the 
younger ages. 

Causative factors in feeble-minded growth. — It has not been 
feasible to include in this study an analysis of the relation of in- 
tellectual growth to causative factors and remedial treatment. 
The general dependence of mental growth upon heredity and 
environment has not been investigated statistically in this study 
The special influences of etiology, medical treatment, and indi- 
vidual physiological anomalies upon the mental development of 
the mental defectives of this investigation have also been passed 
by. A systematic analysis of these influences was planned for in 
the original undertaking, and considerable material was as- 
sembled. But this material proved to be too limited and too in- 
complete to yield positive conclusions. The presentation of this 
material has therefore been omitted as not falling within the 
scope of the present study. But certain generalizations, partly 
theoretical and partly observational, may be outlined as follows : 

(a). There is at present no satisfactory explanation of sudden 
mental arrest in 'at-age' subjects. The most plausible explana- 
tion of this type of 'potential feeble-mindedness' is (1) heredi- 
tary pre-determination or (2) fundamental disturbances in the 
endocrine system. None of the instances of sudden arrest in 
these data are due to traumata or known physiological pathology. 

(b). No definite relation is evident (from the unreported ma- 
terial) between types of development and the known facts of 
heredity or environment. Among the positively hereditary cases 



78 EDGAR A. DOLL 

we find all types of development; similarly for subjects from 
strikingly different environments. Possible qualitative differ- 
ences in intelligence for subjects of different types of parentage 
or environment are not definitely expressed in these quantita- 
tive measurements of gross mental age increases. More careful 
analysis from better data might yield more positive results. 

(c). In traumatic feeble-mindedness there follows ordinarily a 
complete arrest of intellectual growth. The same effect is also 
evident, though with more exceptions, where the mental defect 
is the result of acute disease. 

(d). Special medical treatment has relatively little positive 
effect in bringing about mental growth in these mental defectives, 
even when the retardation is relatively slight or the subject 
young. The beneficial effects of thyroid treatment on cretins at 
certain stages of their development are well-known. No such 
subjects are present in these data. Several of our subjects did 
receive pineal treatment, 'double-dose pineal,' pituitary, and 
'double-dose pituitary.' The number of subjects who improved 
noticeably under such treatment is no greater than the number 
who did not improve under it, and is less than the number who 
improved markedly without special treatment. The subjects 
who received these treatments were relatively young and only 
slightly retarded at the time of treatment. 

(e). The factor of institutional environment is not an ob- 
vious influence in the mental age growth of these defectives, 
either positively or negatively. Sudden arrest takes place in 
good home environment and continued growth occurs within the 
institution. The possible qualitative effects of institutional life 
and accompanying educational acquisition are not obvious in 
these measures of gross mental age growth. 

(f). Undoubtedly individual physiology and anomalies in the 
endocrine system are the most potent factors in individual mental 
growth. This is not only a plausible expectation from general 
bio-chemistry, but is suggested by the results of anthropometric 
measurements and correlated individual physical characteristics. 



THE GROWTH OF INTELLIGENCE 79 

B. Superior Mental Growth 

In a previous section (cf. pp. 20 to 23) certain speculations 
were presented concerning the mental growth of superior chil- 
dren. It will be recalled that the hypothesis was offered that 
during some age-intervals the rate of growth of superior chil- 
dren tends to increase. 

Superior intelligence is defined by Terman as that degree of 
intelligence which may be expressed as an intelligence quotient 
which is above no. An I. Q. above 120 is considered very 
superior intelligence. Obviously, the final or adult I. Q. will 
depend upon the level of intelligence which is accepted as the 
adult average normal. It will also depend upon the efficiency 
of the measuring scale in determining superior deviations of in- 
telligence. If 16 years is taken as the average normal adult level, 
then the highest possible ultimate I. Q. (by the Stanford Scale, 
which measures mental age as high as 19.5 years) is 122. But 
if 13 years is taken as the average adult level, then the ultimate 
I. Q. could be 150. But we have already pointed out the diffi- 
culties in the way of measuring intelligence in terms of mental 
ages which are higher than that of the average normal adult. 

Of course when the 'average adult' and 'superior adult' levels 
of the Stanford Scale are employed to represent the mental ages 
of 16 to 19 years this usage must be recognized as one of con- 
venience only. Terman has recognized this point. He says (31, 
p. 58) : "It will be understood naturally that the numbers ex- 
pressing such mental ages as 17 years, 18 years, 19 years, etc., 
have only a conventional value and are not to be interpreted 
literally. Their use offers a feasible, if arbitrary, method of en- 
abling the superior adolescent or adult to earn a quantitative ex- 
pression of his superiority in the tests." 

If further experimentation should confirm the hypothesis that 
13 years is the average mental age of unselected adults then this 
statement by Terman would apply with equal force to the mental 
ages of 14, 15, and 16 years as well as those beyond. We have 
already indicated (p. 14) that Terman's recent investigations 
tend in this direction. Throughout this study we have used the 
usual 16-year limit for calculating I. Q.'s. 



80 EDGAR A. DOLL 

In either case, > whether we adopt the 1 6-year or the 13-year 
level, there will be for superior children an age of arrest which 
is in part determined by the degree of brightness (the I. Q.), 
in part by life age, and in part by the efficiency limit of the Scale 
as a measure of intelligence. It is therefore peculiarly difficult 
to fix the age of arrest among superior children. The final ap- 
peal must be repeated tests of the same individuals. It is safe 
to assume, however, that the age of arrest is probably not earlier 
than 13 years of age. 

The rate of growth of superior children will depend partly 
upon life age and partly upon the final mental level. As the 
mental age approaches the upper limit of the measuring Scale 
the subject finds it increasingly difficult to maintain his rate of 
development. Hence, after the mental age reaches a certain 
point we may expect the rate of development to decline. When 
a 10-year-old subject tests 15, for example, he has more difficulty 
in maintaining an I. Q. rate of 150 than when he was 6 and 
tested 9, for the scale becomes increasingly more difficult in the 
upper ranges, relatively as well as absolutely. He has less and 
less range of tests over which to register his intelligence. But 
as long as the mental age remains under, say, 15 or 16 years the 
rate of growth will be either a function of age, mental age or 
degree of brightness. 

We have seen that the rate of growth for subjects of subnor- 
mal mentality is a decreasing variable, that is, the inferiority 
tends to become more and more pronounced. And we have 
postulated the converse of this as a speculation regarding su- 
perior children, that is, that up to a certain point (determined 
by the considerations just stated) the rate may be an increasing 
variable and the superiority may become more and more pro- 
nounced. 

Re-tests of superior children. — The literature of the subject 
contains comparatively few reports of repeated tests of superior 
children. Only a few studies, very limited in scope, are avail- 
able. We shall review them later. We are, however, fortunate 
in being able to present some experimental data generously sup- 
plied to us by Miss Anna Gillingham, of the Ethical Culture 



THE GROWTH OF INTELLIGENCE 81 

School, New York City. Miss Gillingham is well qualified in 
the technique of Binet-Simon examining. She has been a close 
student of the several modifications of the Binet Scale and has 
employed the Stanford Revision since its first appearance. In 
particular she has been a student of children of superior mental 
ability and her position as principal of the Primary Department 
and psychological examiner at the Ethical Culture School has 
furnished her with an ample number of subjects. Miss Gilling- 
ham has consented to the use of some of her material in this 
study. This enables us to use the re-examination records of 39 
children whose I. Q.'s were more than no at one or the other 
of two examinations separated by an interval of from one to 
two years. 

We have made certain calculations for 35 of these subjects 
whose life ages at the first examination are between 9 and 12 
years inclusive. For each of these subjects we have calculated 
the life age increment and the mental age increment from the 
first to the second examination. The latter divided by the former 
and multiplied by 100 gives the rate of mental increase for the 
period covered in terms of a percentage of the average normal 
rate. These calculations with other data are presented in 
Table n. 

This table shows for each subject the first life age, first mental 
age, life age increase, mental age increase, rate of increase (as 
a percentage of the average normal rate), first I. Q., and I. Q. 
change. The second life ages may be obtained by adding the 
life age increment to the first life age. Similarly for mental 
age. The second I. Q. may be obtained by adding the I. Q. 
change (retaining sign) to the first I. Q. The subjects are ar- 
ranged by successive ages 9, 10, n and 12 years. They are ar- 
ranged in order of brightness (I. Q.), which is approximately 
also the order of mental age, at each age grouping. The aver- 
ages of Table n are summarized in Table 12. 

Inspection of Tables 1 1 and 12 indicates at each life age 
something of a tendency for the rate of increase to decrease with 
mental age. Unfortunately the number of cases is very small 
and renders any statistical treatment inadequate. Treatment is 



82 



EDGAR A. DOLL 



Ave. 



Table ii 
Repeated Stanford Binet tests of superior children. 



First 



First 



Life Mental Annual 



life 


mental 


age 


age 


rate of 


First 


1. Q. 


age 


age 


increase 


increase 


increase 


I. Q. 


change 


9-5 


12.1 


1.0 


.2 


20 


127 


— 10 


9-5 


12.1 


1.0 


1.8 


150 


127 


+ 3 


9.0 


11.7 


1-5 


2.2 


147 


130 


+ 2 


9.9 


15-6 


•9 


•3 


33 


157 


— 10 


9-7 


15-3 


1.0 


2.9 


290 


158 


+12 


Ave. 9-5 


13-4 


1. 12 


148 


128 


140 


7 


10.8 


II-5 


1.2 


2.1 


175 


107 


4-6 


10.3 


12.0 


1.9 


4-7 


248 


117 


+20 


10.4 


12.7 


•9 


1.0 


in 


122 


— 1 


10.7 


13-8 


1.0 


3-7 


370 


129 


+21 


10.9 


14.1 


1.0 


2.8 


280 


130 


+12 


10.7 


14. 1 


•9 


1.8 


200 


132 


+ 5 


10.7 


14.2 


1.6 


3-3 


206 


133 


+10 


10.4 


14.0 


i-9 


1.5 


79 


135 


— 9 


10.5 


14.4 


1.2 


1.1 


92 


137 


— 4 


10.1 


15-3 


1-3 


•7 


54 


152 


— 12 


Ave. 10.5 


13.6 


1.29 


2.27 


181 


129 


10 


11.6 


"3 


1.2 


4.1 


342 


97 


+37 


11. 1 


12.0 


1.1 


3-9 


350 


108 


+22 


11. 3 


U-3 


i-3 


3-2 


246 


100 


+15 


114 


12.7 


13 


2.4 


185 


in 


+ 8 


1 1.4 


12.8 


14 


1.9 


136 


112 


+ 3 


1 1.2 


12.9 


■9 


.2 


2.2 


115 


— 7 


11.6 


13.8 


i.l 


i-5 


136 


118 


+ 3 


1 1.3 


14. 1 


1-5 


1.9 


127 


124 





1 1.6 


14.4 


2.2 


1.9 


86 


124 


— 6 


1 1.3 


14.2 


2.1 


1.9 


90 


126 


— 6 


11.7 


15.8 


1.1 


.1 


9 


135 


— 11 


11. 1 


151 


1. 1 


•9 


82 


136 


— 5 


"■5 


16.9 


1.0 


1.6 


160 


147 


+ 1 


Ave 1 1.4 


136 


1-33 


1.96 


152 


120 


10 


12.3 


13-6 


1.1 


24 


218 


no 


+ 9 


12.7 


14.1 


•9 


2.6 


289 


in 


+12 


12.4 


14.4 


1.2 


•9 


75 


116 


— 3 


12.5 


14.8 


1-5 


i-5 


100 


119 


— 2 


12.4 


IS-O 


1.2 


•9 


75 


121 


— 4 


12.8 


15-8 


1.1 


2.8 


254 


124 


+ 10 


12.4 


15-5 


1.0 








125 


— 9 



117 



12.5 14.8 1. 14 1.59 145 

rendered still more difficult because of extreme variability in the 
rate of growth. Table 12 shows that the average rate of growth 
fluctuates with age, being a decreasing variable from ages 10 to 
12. But at age 12 the average mental age is higher than at ages 



THE GROWTH OF INTELLIGENCE 83 

Table 12 

Average results of repeated tests of superior children, 

for each life age group. 

Ave. first age 9.5 10.5 11.4 12.5 

Number of subjects 5 10 13 7 

Ave. first mental age 13.4 13.6 13.6 14.8 

Ave. life age increase 1.1 1.3 1.3 1.1 

Ave. mental age increase 1.5 2.3 2.0 1.6 

Ave. rate of increase 128 181 152 145 

Ave. I. Q 140 129 120 117 

Ave. I. Q. change 7 10 10 7 

10 and 11, hence the 12-year decrease in rate may be due to the 
observed tendency of rate to decrease as mental age increases. 

In view of the unreliability of the average rates (due to in- 
dividual variability and the small number of subjects at each 
separate age) it is of some assistance to appeal to correlation 
coefficients for the entire group of subjects. In doing so we 
must not, however, lose sight of the limitation of the correlation 
method when applied to such data. 

The Pearson coefficient of correlation between rate of growth 
and mental age is r = — .30 (P. E. .10), and between rate of 
growth and life age is r = .058 (P. E. .113). The correction of 
these correlations for spurious influence of the correlation be- 
tween age and mental age (r = .058) does not materially change 
the size of the coefficients. The correlation between mental age 
and rate when corrected for constriction remains r = — .30. 
The correlation between life age and rate becomes r = .079. In 
the former case the correlation although not high is fairly de- 
pendable. In the latter case it is low and undependable. 

We may say, then, that in the case of children of superior in- 
telligence between the ages of 8 and 12 years inclusive the rate 
of development is apparently independent of age, that is, it is fair- 
ly constant, except for the influence of mental age. There is only 
a faint and uncertain tendency for the rate to increase with age. 
The rate is, however, somewhat related to mental age during these 
periods. As the mental age increases the rate of growth shows 
some tendency to decrease over the period of 8 to 12 years. We 
cannot determine the age of arrest from these data. The rate 
of growth bcomes increasingly influenced by the upper limits of 



84 EDGAR A. DOLL 

the scale and the upper (hereditarily determined?) final mental 
age of the subject. 

We may conclude, then, that in general the rate of growth of 
intelligence of superior children is conditioned by the mental age 
(or degree of brightness) during the age 8 to 12 years and is 
otherwise relatively independent of age during this period. Pre- 
sumably the rate of growth would decrease after life age 13 
years, since the final mental level of superior children is practi- 
cally attained at that time. At 13 years of age a child of I. Q. 
125 would have a mental age of 16.3, beyond which he would 
find increasing difficulty in obtaining a higher mental age. Even 
though he continued to develop somewhat, his rate would neces- 
sarily fall off rapidly after this point. 



III. CRITIQUE OF THE I. Q. 

Binet and Simon denied that their Scale had any prognostic 
value. They defined subnormality in terms of the amount of 
difference between age and mental age. But they said that with- 
out experimental evidence regarding the course of mental growth 
as determined by successive tests of the same individuals it 
would be impossible to predict future development from a single 
mental age determination. They recognized that some retardates 
might develop and others stand still. They say (2, p. 143) : "No 
actual test can tell us whether an idiot is or is not capable of im- 
provement and to just what point." And again (p. 270) "It is 
understood that these diagnoses (of grade of feeblemindedness 
according to age and mental age) apply only to the present mo- 
ment. He who is an imbecile today, may by the progress of 
age become a moron, or on the contrary remain an imbecile for 
life. One knows nothing of that; the prognosis is reserved." 

About 1 9 12 a group of German psychologists employing the 
Binet Scale expressed dissatisfaction with Binet's method of ex- 
pressing intelligence retardation in terms of the absolute differ- 
ence between age and mental age. Bobertag (4) clearly ex- 
pressed objections to the use of this difference. He presented re- 
sults to show that the distribution of mental ages at each suc- 
cessive life age from 7 to 12 years shows progressively more and 
more 'spread', that is the curves of mental age distribution at 
successive life ages become progressively flattened out. In other 
words the range of variability in years of difference becomes 
more extended with increase of age. Or, in statistical language, 
the P. E. of the mental age distribution increases in size with in- 
crease of age. A deviation of two years above or below the 
median at age 12 was found to occur about as frequently as a 
deviation of one year at age 6. Hence retardation expressed as 
an absolute difference between age and mental age was found to 
be progressively less and less significant with increase of age. 
To overcome this difficulty Bobertag proposed to use the ratio of 



86 EDGAR A. DOLL 

mental age to life age as a more adequate expression of retarda- 
tion. This was termed the 'intelligence quotient' or 'I. Q.' 
Bobertag gives Stern credit for devising and naming this device, 
but Stern acknowledges his indebtedness to Kramer, Chotzen 
and Bobertag. 11 Undoubtedly the I. Q. is, for the reasons given 
by Bobertag, a much more satisfactory way of expressing retard- 
ation than the method of absolute difference. 

About the same time Kuhlmann independently came to sub- 
stantially the same conclusions, but from apparently different 
premises. Kuhlmann gives two reasons for employing relative 
retardation. "One is that the rate of normal mental development 
decreases with age. Mental progress is rapid for the first few 
years and becomes slower as maturity approaches" (22, p. 136). 
This, he believes, is a justifiable premise on the ground of an 
assumed 'rough relationship' between functional mental develop- 
ment and growth in brain weight. Kuhlmann's second argu- 
ment is that "the younger the child is, the less time he has had to 
fall behind the normal in development." Later in life, the in- 
crements of retardation which may have been slight from year 
to year have accumulated into a large total amount. 

Terman has been the strongest advocate of the I. Q. He has 
also produced more evidence than other writers to justify its 
use. We believe, however, that his enthusiasm has developed a 
too optimistic faith in its validity and properties which is not 
entirely warranted by the facts. 

Terman favors the ratio of mental age to life age (instead of 
the difference) as an expression of retardation on the same 
grounds as does Bobertag. He argues that the median deviation 
of mental age increases with increase of age. At life age 12. 
for example, the median deviation of mental age is 2 years 
whereas at age 6 it is only 1 year. In other words, the signifi- 
cance of 1 year of retardation at age 6 is no greater than 2 years 
at age 12. On the other hand he finds that this is not true when 
the mental age distributions are replaced by I. Q. distributions. 

11 One finds it difficult to dissociate the work of these four investigators. 
Their joint work constitutes a coherent whole, the work of each supple- 
menting that of the others. The work of Bobertag is the most pertinent 
for present purposes. 



THE GROWTH OF INTELLIGENCE 87 

In terms of I. Q. the median deviation is approximately constant 
for the succession of life age groups. 

This point may be rendered clear by a statistical table based 
on Terman's results. Table 13 shows the median life ages, 
median mental ages, median I. Q.'s, probable errors of mental 
age and probable errors of I. Q.'s for Terman's unselected school 

Table 13 
Mental age deviation by the Stanford Binet Scale 



No. of 


Median 


Median 


Median 


P. E. of 


P. E. of 


subjects 


life age 


mental age 


I. Q. 


M. A. 


I. Q. 


16 


4.0 


4-1 


103 


.41 


10.3 


54 


5-0 


5-5 


109 


•44 


8.8 


117 


6.0 


6.2 


103 


.48 


8.0 


93 


7.0 


7-3 


104 


.60 


8.5 


98 


8.0 


8.2 


102 


.62 


7.7 


"3 


9.0 


9-1 


IOI 


.69 


7-7 


87 


10.0 


10.3 


103 


■77 


7-7 


79 


II.O 


1 1.2 


102 


1.02 


9-3 


83 


12.0 


11.9 


99 


1.26 


10.5 


98 


130 


12.9 


99 


1.20 


9.2 


82 


14.0 


13-9 


99 


1.16 


8.3 


47 


150 


13-5 


90 


1.16 


7-7 


14 


16.0 


12.8 


80 


i-34 


8.4 



children. The table is made up from calculations based on 
graphs 1 to 11 of Terman's monograph (31). The column of 
Table 13 headed "P. E. of M. A." shows the probable error 
(median deviation plus and minus) of each median mental age, 
that is, the range above and below the median which includes the 
middle 50 per cent of subjects when arranged in order of as- 
cending mental age values. Similarly for the column headed 
"P. E. of I. Q." 

The P. E. of M. A. values are observed to increase steadily 
and regularly with increase of life age from about .4 at age 4 
to about 1.2 at age 12. This means that a deviation plus or 
minus of 1.2 occurs as frequently at age 12 as a deviation plus 
or minus of .4 at age 4. In other words, a deviation of 1.2 years 
of mental age at age 12 has (for average normal unselected 
subjects) the same significance as a deviation of .4 years at age 4. 

The values of P. E. of I. Q. on the other hand are fairly equal 
at all successive ages, ranging from approximately 8 to approxi- 
mately 10 points. In other words, the median deviation from 



88 EDGAR A. DOLL 

the standard I. Q. is about the same at all ages, being on the 
average about 8.5 points I. Q. 

Therefore, it is argued (the course of Terman's argument be- 
ing slightly different from ours) that the I. Q. is a better unit 
of mental deviation than is the amount of difference between 
actual mental age and the standard mental age for any given 
life age. 

Thus far the argument is fairly obvious and sound. It is clear 
that the I. Q. furnishes a better unit of deviation than does the 
amount of difference between actual mental age and standard 
mental age when it is a question of determining relative bright- 
ness or the significance of retardation or acceleration. But we 
cannot go so far as to conclude from this single merit of the 
I. Q. that, "The mental age of a subject is meaningless if con- 
sidered apart from chronological age. It is only the ratio of re- 
tardation or acceleration to chronological age (that is, the I. Q.) 
which has significance" (30, p. 68). 

Mental age is an absolute measure and has great significance even apart 
from age, although, to be sure, one may not ignore life age. If we know 
that the mental age of an individual is 10 years, for example, we know, 
whatever his chronological age may be, that he could (at the time) prob- 
ably do about 4th grade school work, could learn any of the simple manual 
arts and trades, could master the relatively unskilled industrial occupations, 
could control his own conduct and work with only a small amount of super- 
vision, and so on. Of course we would want to know his actual life age, 
his degree of brightness, his intellectual maturity and activity, his physical 
condition, temperament, personal history and so on, but even without these 
latter facts his mental age would tell us a very great deal about his actual 
and probable scholastic, industrial, and social capabilites. 

But suppose we know only that the I. Q. of an individual is 100. We 
then know only that he is of average normal brightness. Not knowing his 
absolute mental age, whether it is 5, 10, or 15 years, we cannot say anything 
about his capabilities. Or suppose his I. Q. is 50. We would know he is 
probably feeble-minded but we would not know of what degree, whether 
idiot, imbecile or moron. Therefore, while the I. Q. is admittedly valuable 
as a measure of brightness, if we use it apart from age or mental age it 
tells us nothing about capabilities pro tern. Of course neither mental age 
nor I. Q. should be used apart from life age, but if life age is to be ig- 
nored it is the I. Q. which loses meaning and not the mental age. 

The errors to which the uncritical use of the I. Q. may lead are many and 
serious. Terman for example concludes (30, p. 67) : "The traditional view 
that variability in mental traits becomes more marked during adolescence is 



THE GROWTH OF INTELLIGENCE 89 

here contradicted, as far as intelligence is concerned, for the distribution of 
I. Q.'s is practically the same at each age from 5 to 14 years! 2 For example, 
6-year-olds differ from one another fully as much as do 14-year-olds." But 
we have just shown (cf. Table 13) that in terms of absolute intelligence in- 
dividual differences in mental age constantly increase. The P. E. of M. A., 
which is the measure of variability in actual intelligence, is at age 14 almost 
exactly three times as great as at age 4. It is only when we have changed 
these absolute units to relative units that individual differences are found 
not to increase with age. 

Many studies in the field of juvenile delinquency cannot properly be evalu- 
ated because the results are expressed only in I. Q. terms without accom- 
panying data in regard to the ages of the subjects (cf. for example various 
studies in the Journal of Delinquency). It is possible that types of crime 
are related to the intelligence of delinquents. What are the crimes com- 
mitted by an I. Q. of 75, for example? The answer will depend on whether 
the I. Q. is obtained from the ratio 12/16 or 9/12. Or suppose it is a ques- 
tion of diagnosis, and suppose the investigator has used an upper mental 
age limit which is unacceptable to some authorities. The question imme- 
diately arises concerning the number of subjects who were above the mental 
age limit in question. This question cannot be answered from an I. Q. 
frequency distribution if it is unaccompanied by a statement of life ages 
or mental ages. 

It is therefore obvious that we cannot afford to ignore the 
actual mental age or life age from which an I. Q. is calculated. 
To do so may invalidate a study on the basis of classification. 
The I. Q. may be a practical unit for measuring 'brightness' at 
a given age or for comparing degrees of brightness at different 
ages. But it cannot serve as a satisfactory measure of degree of 
intelligence independently of the ratio from which it has been 
derived. These fairly obvious objections to the I. Q. have been 
repeatedly pointed out but seem to have been generally ignored. 

Constancy of the I. Q. — We have seen that the I. Q. is valu- 
able as a measure of relative brightness, and as a unit of mental 
deviation. Its significance is superior to mere difference between 
age and mental age as a measure of retardation. 

What is the value of the I. Q. as a prognostic device, that is 
as a means of prediction? What is its value as a means of ulti- 
mate diagnosis or classification of such significant intellectual 
types as feeble-minded or gifted children? May it be used as a 
predictive measure of rate of development? 

12 Italics ours. 



90 EDGAR A. DOLL 

We have showed that the I. Q. as the probable error of mental 
age is approximately constant at all ages. In other words, the 
I. Q. distributions are practically identical at all ages from 4 
to 14. It follows as a corollary that on the average the I. Q. is 
constant as a measure of rate of growth during the ages 4 to 14 
years. This is because the average normal annual mental age 
increment from age to age is approximately 1 year. This is a 
consequence of the empirical nature of the standardization of the 
measuring scale, which is so devised that each median mental 
age will equal its corresponding median life age. Hence the 
median annual increment is always 1 year (from ages 4 to 14). 

We define rate of growth as this annual mental age increment, 
that is, the amount of mental age increase divided by the cor- 
responding life age increase. Since for the average normal sub- 
ject this increment is on the average 1 .0/1.0 we may convert 
other rates to a percentage of the average normal by multiplying 
a given rate by 100. Thus if a subject gains .5 years in one 
year his rate of increase in terms of a percentage of the aver- 
age normal subject is : rate = — x 100 = .50 per cent (of the 

1.0 

average normal annual rate). 

An objection might be raised against this definition on the ground that 
the actual rate of growth is not 100 at all ages. The actual median rates 
(calculated from Table 13) are as follows: 

Age-interval 4-5 5-6 6-7 7-8 J8-Q. 9-10 10-11 11-12 12-13 13-14 
Median rate 140 70 no 90 90 120 90 70 100 100 

That the actual rate is not 100 is, however, only an experimental inaccuracy 
of standardization. The principle of standardization calls for a rate of 100 
which is only approximately obtained by experiment. 

Another objection is that the average rate of growth after age 16 (or 
after 13 if we accept Doll's hypothesis) is found to be instead of 100, since 
after this age there is no increase in mental age level of higher age groups. 
But for experimental purposes it was necessary to assume continuous growth 
to an indefinite age. It was conceivable that the feeble-minded might con- 
tinue to increase in mental age after the age at which average normals cease 
to increase. 

We have not been free to use the I. Q. as a measure of rate 
of increase because this would have committed us to certain as- 
sumptions whose very validity we intended to question. More- 



THE GROWTH OF INTELLIGENCE 91 

over, the I. Q. tends to obscure fluctuations in rate of increase 
because the variations are distributed over a period of years. 
The I. Q. is always a total average rate for the age of the sub- 
ject. Hence the fluctuations in mental growth from year to year 
are 'ironed out' by the I. Q. mode of expressing mental growth. 
This ironing out or 'smoothing' process becomes more and more 
effective as age increases. Suppose a child at the age of 9 years 
has a mental age of 9, which is an I. Q. of 100. And suppose 
that during the next year this child makes absolutely no mental 
age gain. His I. Q. at 10 years would then be 90. The loss of 
I. Q. would be only 10 points. Yet the loss in actual rate of 
growth is 100 points, for the 9-year I. Q. rate has dropped from 
expected 100 to actual o. This loss of 100 points is by the I. Q. 
method spread over the entire 10 years, giving an apparent loss 
in rate of only 10 points for the year. If this hypothetical child 
were then to gain 2 mental years from age 10 to age 11 his I. Q. 
gain would now be only 10 points; although he would actually 
be gaining at twice the normal rate, or 200 per cent, this rate 
would be minimized in the I. Q. The irregular development of 
this subject from 9 to 11 years showing first absolute arrest and 
then twice normal gain would appear only as a slight irregu- 
larity in his growth by the I. Q.'s. 

Hence it follows that the I. Q. is not a valid measure of rate 
of growth since it distributes variations over a period of years 
instead of measuring them only for the time-interval under con- 
sideration. It also follows that apparently slight variations in 
I. Q. such as would be considered 'approximately negligible' may 
actually be on the contrary very significant. It also follows that 
equal amounts of I. Q. variation have different meanings as 
measures of rate of growth according to the ages of the sub- 
jects. Thus, zero increase in mental age between 3 and 4 years 
of age would effect an I. Q. reduction of 25 points for that 
interval (assuming I. Q. 100 at age 3), while between 13 and 
14 years the reduction would be only 7 points. And we have 
seen that while the median rate of mental age increase may vary 
from age to age this variation is not evident in the I. Q. 

Literature on the constancy of the I. Q. — Bobertag was one 



9 2 EDGAR A. DOLL 

of the first to conduct re-examinations of the same subjects (4). 
His results showed that the Binet Scale (1908 version) is valid 
for this purpose. He found no significant influence of memory 
or 'practice' from the first examination. His results showed a 
close relation between the mental age ranks of the first and sec- 
ond examinations, a correlation of R = .95. Moreover, the 
'at-age' children (retardation or acceleration less than 1.0 year) 
gained on the average 1 year in mental age during 1 year of 
time, the retarded children gained only two-thirds of year, and 
the superior children gained a year and a quarter (4, pp. 521 ff). 
His results also showed that the older subjects (11 and 12 years 
of age) gained less than the younger subjects (7 and 8 years of 
age) . This result he ascribed to the increasingly narrow range of 
tests in which the older subjects could register improvement. 
This tends to explain the fact that 1 subject dropped from 'ac- 
celerated' to 'at-age,' and 4 subjects from 'at-age' to 'retarded.' 
Unfortunately the actual ages of his individual subjects were not 
presented for each test-age and it is therefore not possible to de- 
termine the rate of growth at the different ages. Bobertag con- 
cludes (p. 528) : "Children whose intelligence is above average 
gain more rapidly than those whose intelligence is average, while 
those below average gain more slowly than those who are aver- 
age. Therefore, the difference from the average plus and minus 
must increase with increase of age. Also, within the group of 
those who are average it must come about that some who are 
average must become retarded and some become advanced (in 
units of the difference between the actual mental age and the 
standard mental age for the life age of the subject)." Bobertag 
employs this conclusion as an argument in favor of the use of 
the I. Q. ratio in preference to the difference between mental 
age and life age. He also contends that the I. Q. must be used in 
place of mental age difference for designating feeble-mindedness 
and the several grades of feeble-mindedness. 

But with regard to the constancy of the I. Q. as a measure of 
individual development from year to year Bobertag has this to 
say: "If one limits himself to a few successive ages, e.g., 8, 9 
and 10 years, then one would be warranted in calculating in 



THE GROWTH OF INTELLIGENCE 93 

each case after the manner just described (for employing the 
I. Q.). One would then be able to say that the I. Q. is approxi- 
mately constant, being about .75 for moronity and about .65 for 
imbecility (the exact figures being for the moment immaterial). 
But if one reviews a series of ages, such as the entire period of 
the child's development of intelligence, then it is very question- 
able whether the hypothesis that the I. Q. is constant is valid." 
He then proceeds to raise several objections against the assump- 
tion of the I. Q. being a constant in individual development, 
to wit : 

( 1 ) . The younger the child the more difficult it is to determine 
individual differences in intelligence. Individual differences in 
a scale of mental tests are so small in amount early in life that 
one cannot measure them with a high degree of accuracy, al- 
though later in life it is possible to do this. It is therefore hardly 
possible to diagnose feeble-mindedness in children who are very 
young. And the less the degree of subnormality the more diffi- 
cult it is to effect diagnosis early in life. And the same is true 
of supernormal children. 

(2). The idea of feeble-mindedness as a condition of heredi- 
tarily limited development of intelligence lends color to the 
theory that among the feeble-minded intelligence growth be- 
comes uniformly more and more retarded, "like the progress of 
a stone thrown vertically into the air." Mental defect, there- 
fore, is not absolute from age to age but increases relatively 
with increase of age (although there is a lack of positive data 
to prove the point). 

(3). The results of Chotzen with children from the Hilfschule 
show a decrease in I. Q. from age to age for children who are 
more than 3 years retarded mentally. 

From these considerations Bobertag concludes that the growth 
curves of the feeble-minded are not retarded by an amount which 
is constant from birth to maturity but follow the course of a 
decreasing variable. And he finds this to be true whether the 
growth curve of the average normal subject is taken as a straight 
line or as a curved line (cf. our Figs. 1, 2 and 3). He concludes 
his analysis with a graph showing the comparative growth curves 



94 EDGAR A. DOLL 

of moron feeble-mindedness, assuming I. Q. as a constant or as 
a decreasing variable. In the latter case the moron has at age 
4 an I. Q. of 85, at age 8 an I. Q. of 75 and at age 12 an I. Q. 
of 67. 

Stern (28) recapitulates the work of Bobertag, Kramer and 
Chotzen but adds little to it. In our judgment Bobertag's is the 
clearer exposition. Stern's argument regarding the constancy 
of the I. Q. applies principally to the feeble-minded. He finds 
that the I. Q. is a better expression of mental retardation than 
is the difference between mental age and life age. But from a 
survey of the work of Chotzen, Kramer and Bobertag he con- 
cludes as follows (28, p. 83 f.) : "The quotient does not seem, 
however, to' afford an actually constant expression of degree of 
feeble-mindedness, but shows a tendency to fall in value as age 
increases. This tendency, it is evident, is but slight within the 
limits of age that have been mentioned (8 to 12), so that for 
many problems it can be neglected. Before and after these ages 
the fall in the value seems to take place more rapidly. In the 
case of the later age-levels this is easily intelligible, for once the 
stage of arrest ... is reached . . . the quotient . . . must de- 
crease as chronological age increases. The feeble-minded child, 
it must be remembered, not only has a slower rate of develop- 
ment than the normal child, but also reaches a stage of arrest 
at an age when the normal child's intelligence is still pushing 
forward in its development. . . . From these considerations it 
follows that the intelligence quotient can hold good as an index 
of feeble-mindedness only during that period when the develop- 
ment of the feeble-minded individual is in progress. The above- 
mentioned gradual tendency of the mental quotient to sink dur- 
ing the progress of development shows that this development 
approaches the final level of arrest at a progressively decreasing 
rate. Whether we shall succeed in finding a formula for a truly 
constant coefficient of feeble-mindedness must be left for the 
future." He quotes Kramer as doubting the possibility of ac- 
complishing this. 

This position of Stern with respect to the age of arrest and 
the decreasing rate of development is fully supported by our 



THE GROWTH OF INTELLIGENCE 95 

own experimental investigation on re-tests of feeble-minded. 
But we may add that the I. Q. is apparently constant at certain 
age-intervals only because a short segment of a somewhat flat 
curve approximates a straight line. Moreover, the I. Q. sinks 
only gradually even after the age of arrest because, as we have 
pointed out, the true loss in rate of growth is minimized by the 
I. Q. mode of expressing rate of growth. It should also be re- 
called that Stern is writing of the average feeble-minded types 
and not of individual feeble-minded subjects. For the in- 
dividual subject the rate of retardation is sometimes a rapidly 
decreasing variable, sometimes a slowly decreasing variable and 
sometimes a constant. 

Kuhlmann (22) developed the principle of the I. Q. on 
grounds different from those of Bobertag and Stern. Kuhl- 
mann bases his principle of the ratio of mental age to life age 
on two 1 main assumptions, namely, (1) that the rate of mental 
development is not a decreasing variable but is constant through 
a succession of ages, and (2) that "feeble-mindedness is simply 
a retarded rate of development whose ratio to the normal remains 
constant" (p. 138 f.). He recognizes that the first of these as- 
sumptions is somewhat in error and is contrary to his own pre- 
vious argument that the rate of growth (in absolute units) is a 
decreasing variable. Kuhlmann adopts an empirical scale of 
average normal mental ages which are identical age for age 
with their corresponding life ages. Assuming that the feeble- 
minded rate is at all ages a constant ratio to the average normal 
rate, he works out a scale of mental ages for these ratios. "The 
practical usefulness of this scale depends not on whether it is 
entirely correct, but on whether it represents the facts more 
closely than we can determine readily in any other way" (p. 140). 

In a later article (23) Kuhlmann questions the conclusions 
of Bobertag and Stern that there is an age of arrest for feeble- 
minded subjects which is sometimes prior to 15 years. He 
states that this is an assumption having no warrant in fact and 
that his own data "rather indicate that many cases continue to 
develop, some even beyond the age of fifteen." He also chal- 
lenges Bobertag's conclusion that feeble-minded subjects develop 
at a rate which steadily decreases. 



9 6 EDGAR A. DOLL 

Terman has from the first emphasized that the I. Q. is a con- 
stant, at least for ages 4 to 14 years, if the I. Q. is based on the 
Stanford Scale. In his Measurement of Intelligence (30) he 
says (p. 63) : "Re-tests of children by the Standard Revision 
have been found to yield intelligence quotients almost identical 
with those secured from two to four years earlier by the same 
tests. Those who graded feeble-minded in the first test graded 
feeble-minded in the second test; the dull remained dull, the 
average remained average, the superior remained superior, and 
always in approximately the same degree. . . . The average dif- 
ference between the I. Q. obtained in the second test and that 
obtained in the first was only 4 per cent (4 points I. Q.) and the 
greatest difference found was only 8 per cent." 

In a later work (31), while maintaining that the I. Q. tends 
to remain approximately constant on the average as determined 
by re-tests of individual children, he says (p. 56) : "The most 
marked exceptions to this rule are found with the feeble-minded, 
whose intelligence quotient shows a tendency to decrease con- 
siderably." 

The data upon which these conclusions were based are not 
presented in either publication and we are therefore unable to 
evaluate them. But in a more recent work (29) data are pre- 
sented which show the results of repeated tests with 315 chil- 
dren. Forty-six subjects had been examined 3 or more times. 
"In case of a child tested several times, each test has been com- 
pared with each of the others; for example, the first test with 
the second, third and fourth separately, the second test with the 
third and fourth separately, and the third test with the fourth" 
(p. 138). This mode of treatment yields 120 I. Q. comparisons 
for the 46 subjects tested more than twice, or a total of 435 I. Q. 
comparisons at intervals of from one day to seven years as fol- 
lows: 

Less than 1 year 86 

1 to 3 years 138 

3 to 5 years 85 

More than 5 years 127 



THE GROWTH OF INTELLIGENCE 97 

The ages of the subjects, counted at the time of the earlier of 
two compared tests were as follows : 

3 to 5 99 

6 to 8 139 

9 to 11 134 

12 to 14 55 

Above 15 8 

A table is presented (p. 141) showing the relation of I. Q.- 
change to time-interval between tests, age at first test, and I. Q. 
It is apparent from this table that I. Q. change is almost wholly 
independent of time-interval, age, or degree of brightness. The 
table is summarized as follows (p. 142) : 

"(1) The central tendency of change is represented by an 
increase of 1.7 in I. Q. ; 

(2) The middle fifty per cent of changes lies between the 
limits of 3.3 decrease and 5.7 increase; 

(3) The probable error of a prediction based on the first test 
is 4.5 points in terms of I. Q." 

Another table shows the correlation distribution of I. Q.'s at 
first and second tests. The correlation between I. Q.'s is 
r — .933. There are no marked differences in the medians of 
either series. At each I. Q. interval, however, there are ap- 
proximately twice as many subjects whose second I. Q. is 5 
points or more above the first I. Q. as there are subjects whose 
second I. Q. is 5 points or more below the first I. Q., indicating 
a constant tendency for the I. Q. to increase at the second ex- 
amination. 

The author points out that there are few feeble-minded sub- 
jects and that these are relatively high-grade types. Hence it is 
recognized that : "It is possible that feeble-minded children test- 
ing below I. Q. 60 are less likely to hold their own than those of 
milder degree of defect." It is also pointed out that superior 
I. Q.'s may be expected to decrease after 13 or 14 years be- 
cause their mental ages will be higher than the Scale can ade- 
quately measure. But in a succeeding chapter (p. 191) it is 
stated that: "re-tests of superiors show that the I. Q. is more 
likely to increase" in spite of the tendency for I. Q.'s of the 



98 EDGAR A. DOLL 

older superior subjects to decrease. "The central tendency [of 
I. Q. change for superior children] was toward a gain of 2.08 
points." 

Significance of I. Q. changes. — It must be recognized from 
this brief summary of Terman's latest work that for his data 
at least the I. Q. is approximately constant on the average and 
is practically independent of age, mental age and time-interval. 
But we may well question two aspects of the I. Q. It is only 
approximately constant and only constant on the average. If we 
desire to apply the I. Q. to individual subjects as a measure of 
predictive rate of growth we must know the probability of con- 
stancy and the meaning of approximateness. 

We have already pointed out that absolute mental age is more 
significant for practical purposes than I. Q., the former being a 
measure of present or actual capability while the latter is a meas- 
ure of deviation and (when constant) of ultimate or potential 
capability. Given an I. Q. 100, for example, we do not know 
in what school grade such a child belongs, but given a mental 
age of 10 years we can say he belongs (other considerations 
aside) in the fourth school grade. 

We have also pointed out that slight variations in successive 
I. Q.'s may be accompanied by marked variations in annual rates 
of development. In our Table 5, for example, the I. Q. is within 
10 points (plus or minus) of the rate only in about 20 per cent 
of subjects. 

Complete absence of mental age increase between 3 and 4 
years of age brings a decrease of 25 points in I. Q. while com- 
plete absence at 15 to 16 brings a decrease of only 6 points (cf. 
p. 91). Hence the significance of I. Q. deviation depends upon 
the age of the subject. A gain of 5 points after 10 years of age 
indicates a marked change in rate of mental age increase while 
before that age it is progressively less and less significant. Hence 
the curve of mental age growth may be very irregular while the 
I. Q. is slightly modified, or it may be regular and the I. O. 
obviously modified, according to the age of the subject. If 'nas- 
cent stages' occurred they might be completely lost sight of even 
when I. Q. is approximately constant over a long interval. Thus 



THE GROWTH OF INTELLIGENCE 99 

a subject who made 100 per cent progress up to 10 years of age 
and 50 per cent thereafter would at 15 years have lost only 17 
points I. Q. Another subject with I. Q. at 100, for example, 
might make no gain from 10 to 12 and then double gain from 
12 to 14 (a 'nascent stage') and yet have an I. Q. constant at 
100 for both ends of the four-year period, and varying only by 
17 points at the middle of the period. 

The significance of I. Q. deviation and a criterion of approxi- 
mate constancy of the I. Q. may be derived empirically some- 
what as follows. The principal age ranges within which the 
I. Q. is considered constant are from, say, 6 to 14 years. If 
we admit that a deviation of 50 per cent from the average 
normal annual rate of growth is a significant deviation then we 
obtain during successive years the following significant I. Q. 
deviations : 

Life age 6789 10 11 12 13 14 

Significant I. Q. deviation 87665 5444 

In other words, for the range of ages as a whole an I. Q. devi- 
ation of about 5 points plus or minus will register a change of 
50 per cent in the average normal annual rate of mental age in- 
crease. For feeble-minded subjects a lesser I. Q. change would 
signify an equally significant change in rate while for superior 
subjects a higher change would be necessary. If a subject's I. 
Q. had been constant at 50 up to 10 years of age and his rate 
were then reduced 50 per cent of its constant value, this would 
be indicated by a loss of only 2 points in I. Q. at age n. On 
the other hand a superior subject developing at a constant I. Q. 
150 until age 10 and then increasing that rate 50 per cent of its 
value would show an I. Q. gain of 6 points in I. Q. at age 11. 

In general, then, an I. Q. change of 5 points or more is a 
significant I. Q. change. That is, we may define approximate 
I. Q.'s as those which change by less than 5 points. A deviation 
of 10 points is very significant if the life age is high (above 10) 
or if the I. Q. is low (below 75). 

Stating the matter statistically instead of by empirical argu- 
ment we may say that any deviation greater than P. E. is sig- 



ioo EDGAR A. DOLL 

nificant. The P. E. of I. Q. change for Terman's data is 4.5 
points (29, p. 142), which is the same as we get by practical 
deduction. 

Assuming, then, that an I. Q. change of 5 points is a signifi- 
cant deviation, how frequently will it occur ? Terman has calcu- 
lated both the theoretical frequencies and the actual frequencies 
for several multiples of P. E. (29, p. 148). The actual prob- 
abilities are 1 to 1 (50 per cent) that the I. Q. change will not 
be more than 5 points plus or minus; 5 to 1 that it will not be 
more than 10 points plus or minus; and 16 to 1 that it will not 
be more than 15 points. Or: "We may say, roughly speaking, 
that the chances that an I. Q. will either increase as much as six 
points or decrease as much as four points are one in two; that 
it will either increase as much as twelve points or decrease as 
much as eight points, one in five; that it will either increase as 
much as eighteen points or decrease as much as twelve points, 
one in twenty ; that it will increase as much as twenty-four points 
or decrease as much as sixteen points, one in a hundred and 
forty" (29, p. 149). 

In brief, every second child has a significant I. Q. change, every 
fifth child a very significant change, every twentieth child an ex- 
tremely significant change, and so on. Or, the I. Q. is approxi- 
mately constant only for every other child; that is to say, the 
rate of growth of every other child changes as much as 50 per 
cent of the average normal rate for a single year. 

But there is a fallacy in this argument. A deviation of 5 
points over a period of one year has not the same significance as 
a deviation of 5 points over a period of 5 years. Hence the 
meaning of approximateness depends upon the time-interval be- 
tween tests. A child with an I. Q. of 100 at age 6 who developed 
at a rate of 50 per cent thereafter would lose 23 points in 5 
years, having an I. Q. of JJ at age 11, while a child 10 years old 
under the same conditions would lose only 17 points. But if a 
50 per cent loss in rate of growth for one year is serious, such 
a continued loss for 5 years would be very serious indeed. 
Hence, 17 points loss after 5 years would be a certain multiple 
of the 'seriousness' of 5 points less in 1 year. 



THE GROWTH OF INTELLIGENCE 101 

Refutation of the constancy of the I. Q. — We may now briefly 
review our own experimental data in relation to the I, Q. We 
have shown that 63 per cent of all our feeble-minded subjects 
who are under 15 years of age at first examination do not im- 
prove mentally as much as one year in at least 3 to 5 years. The 
individual average annual rate of development for these sub 
jects in most cases is less than 20 per cent. This is in spite of 
the fact that most of the first I. Q.'s of these subjects at the first 
test range above 50. Nearly two-thirds of the subjects under 
15 make no more mental progress than do the subjects who are 
15 years and older. 

We have also shown that this arrest of development is a func- 
tion of the final mental age of the subjects, and that the rate of 
development, even for those subjects whose mental age is increas- 
ing, decreases regularly (on the average) with age from 8 to 14 
years. Our Table 5 has shown that at any age there are never 
more than about 20 per cent of subjects whose I. Q.'s agree 
within 10 points plus or minus with the corresponding annual 
rates of growth. And our Table 7 has shown that even for the 
37 per cent of subjects under age 15 who are increasing in 
mental age at least one year in five the I. Q. after 4 years is at 
least 10 points lower in more than half of the cases. And we 
have shown further that I. Q. change in the feeble-minded is in- 
dependent of mental age except for a tendency for more low- 
grade feeble-minded than high-grade to maintain an approxi- 
mately constant I. Q. 

On all these issues our data are superior to other data on 
feeble-minded subjects yet published and certainly make tenable 
the hypothesis that for feeble-minded subjects the I. Q. is on the 
average a steadily decreasing variable after the age of at least 
8 years. This hypothesis was advanced by Bobertag and Stern 
in 1 912. It was also advanced by Goddard at the same time and 
received confirmation in a preliminary report of the present data 
in 1913 (cf. 17). The clinical applications of this point of view 
are admirably presented in a recent article by Mateer (25) which 
is in certain respects a more detailed critique of the clinical value 
of I. Q. than we have felt free to undertake in this study. 



ios EDGAR A. DOLL 

With respect to superior children our data are distinctly 
limited. Yet we have been able to show marked discrepancies 
between the I. Q. predicted rate of growth and the actual rate 
of growth, for relatively short time-intervals (one to two years). 
Among 35 children with I. Q.'s above no we found rates of 
mental age increase varying from zero to plus 350, in the latter 
case the rate being 3 times the predicted rate. Moreover, we 
also found the average rate of growth at ages 10, n, and 12 
to be distinctly higher than the average I. Q., showing a tendency 
for the superiority to increase. 

Results similar to ours for the feeble-minded may be cited 
from the literature. Goddard (15) found that after three an- 
nual examinations of 346 feeble-minded children 32 per cent 
had made 'no variation whatever,' while 67 per cent varied less 
than 0.5 years. Only 28 per cent seemed to have made some 
progress but in many of these cases the progress was only due 
to 'normal variation of the abnormal mind.' Only 6 per cent 
gained more than 1.0 years in the two years covered by the three 
testings. These were all 'younger cases' (17). Since Goddard's 
subjects were distributed about equally above and below 15 years, 
his results would show that about 10 to 15 per cent of his sub- 
jects who were below age 15 had improved more than 1.0 year 
in 2 years. Similarly, about 85 to 90 per cent of those who were 
below 15 years improved at a rate of less than 50 per cent of 
the normal. 

Berry (1) also reported results in 1912 on re-tests. His sub- 
jects were 42 normal public school children, principally 8 and 9 
years old, and 40 institutional feeble-minded, aged 9 to 24 years. 
The normal subjects made an average gain of 1.0 year, average 
deviation .26 years, with individual gains ranging from .4 years to 
1.8 years. The feeble-minded subjects (mental ages 4 years to 
11 years) made an average gain of .5 years, average deviation 
.31 years, with individual gains ranging from — .6 years to +1.2 
years. Four subjects, all under 15 years of age, gained 1 year 
or more, which is a rate of increase considerably higher than the 
I. Q. prediction for these subjects whose I. Q.'s were presumably 
below 75. (A similar result is also shown in several of our own 



THE GROWTH OF INTELLIGENCE 103 

subjects, 9 of whom gained at the rate of 90 to no for a single 
year) . 

Individual irregularity of development. — An excellent report 
of mental growth of the feeble-minded was published in 191 5 by 
the Bureau of Analysis and Investigation of the State of New 
York (26). The ages and mental ages of 52 borderline feeble- 
minded subjects are shown graphically in such a way as excellent- 
ly to illustrate the marked differences in growth of the individual 
subjects. These graphs are reproduced here as Fig. n. From 

Table 14 

Results of repeated tests of borderline feeble-minded; sample treatment of 

first 10 subjects in reference (26). 

Life Mental Annual 



Subject 


Life 


Mental 




age 


age 


rates of 


I.Q. 


No. 


ages 


ages 


I. Q.'s 


increases 


increases 


increase 


changes 


1 


3-6 


3-0 


83 












4.8 


4.6 


96 


1.2 


1.6 


133 


+ 13 




5-7 


5-2 


91 


•9 


.6 


67 


— 5 


2 


5-7 


5-0 


88 












74 


7-0 


95 


i-7 


2.0 


118 


+ 7 




8.4 


7-6 


9i 


1.0 


.6 


60 


— 4 


3 


6.0 


6.0 


100 












7-0 


7.0 


100 


1.0 


1.0 


100 







7-9 


8.2 


104 


•9 


1.2 


133 


+ 4 




9.0 


9.0 


100 


1.1 


.8 


73 


— 4 


4 


5-i 


4.4 


86 












6.1 


5-2 


85 


1.0 


.8 


80 


— 1 


5 


4-3 


3.6 


84 












5-2 


3.8 


73 


•9 


.2 


22 


— 11 




6-3 


5-6 


89 


1.1 


1.8 


164 


+16 


6 


6.4 


4.4 


69 












7-3 


6.0 


82 


•9 


1.6 


178 


+13 




84 


7.0 


82 


1.1 


1.0 


9i 


+ 1 


8 


8.0 


7.0 


88 












8.8 


7-4 


84 


.8 


•4 


50 


— 4 




9.8 


7.2 


74 


1.0 


— .2 


— 20 


— 10 


9 


4-5 


3-4 


76 












5-5 


4.8 


87 


1.0 


1.4 


140 


+11 


10 


8.5 


6.2 


73 












9-3 


7.0 


75 


.8 


.8 


100 


+ 2 




10.3 


7.2 


70 


1.0 


.2 


20 


— 5 


11 


9-8 


8.0 


82 












11.2 


8.8 


79 


i-4 


.8 


57 


— 3 




12.2 


10.2 


84 


1.0 


1.4 


140 


+ 5 



104 



EDGAR A. DOLL 



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mental ages, unshaded areas life ages. (From ref. 26.) 
Fig. 11 — Section A. 



THE GROWTH OF INTELLIGENCE 



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D«« .v»- 
0<.» .*.» 








0t« .^iS 
















Oct >v- 
0t.. V 5 

















Chart Showing Mental and Physical Ages op 52 Children With Dates 
op Examination- Nos. 18-34. 

Mental age development in 'borderline' subjects showing arrested growth 
before io years of age with consequent decrease in I. Q.'s. Shaded areas 
show mental ages, unshaded areas life ages. (From ref. 26.) 
Fig. 11 — Section B 



106 EDGAR A. DOLL 

this material we have made calculations for the first 10 cases 
(excluding case 7 because of an error) which are presented in 
Table 14. This table shows the marked fluctuations which take 
place from year to year in annual rate of growth while the I. Q.'s 
remain approximately constant. The lack of agreement between 
I. Q. as a predicted rate and the actual rate for annual periods is 
obvious from this table. 

Inspection of Fig. 11 shows very clearly complete arrest of de- 
velopment for two subjects under 10 years of age (mental ages 
7 and 5 ) . Complete arrest is also shown for four additional sub- 
jects whose ages are under 12 years (mental ages about 7). 
Since the subjects are all doubtfully feeble-minded at the first 
test these results are particularly striking. Our own results on 
potentially feeble-minded case shows similar effects with longer 
time periods (cf. Table 5). 

Striking results for individual feeble-minded subjects were also 
presented by Mateer (25). Curves of mental age growth were 
plotted for 8 subjects whose I. Q.'s at the first examination 
ranged from 98 to 104. Four subjects whose initial life ages 
were 7 years made less than one year of mental age increase in 
four years. Another subject made no progress the first year and 
then made 100 per cent progress per year for 3 years. Another 
made no progress for 2 years and then 70 per cent progress for 
2 years. Dr. Mateer concludes that an individual's I. Q. "may 
decrease steadily through even the earlier years, it may stand 
still, or it may even temporarily increase." 

The writer has elsewhere (9) presented several case records of 
mental ages designed to show that for any grade of feeble- 
mindedness I. Q.'s may decrease steadily from I. Q. 100 or temp- 
orarily increase when markedly under 100. This paper also 
indicated marked fluctuations of I. Q. among normal subjects. 
In another paper (10) the writer has defined 'potential feeble- 
mindedness' as a type of feeble-mindedness where the I. Q. is 
close to 100 in early tests but drops rapidly in later tests (cf. 
successive I. Q.'s in Fig. 9). 

Finally we offer from the experimental data of the present 
study graphic results of individual feeble-minded subjects. 



THE GROWTH OF INTELLIGENCE 



107 




108 EDGAR A. DOLL 

Growth curves of particular developmental types are presented 
in Figs. 12 to 15. These curves are 'smoothed' (as described on 
page 42) and are therefore more regular than they would be if 
we had used the original mental ages. This smoothing enables 
us to plot uniform age-periods which makes the calculations 
simpler and the comparisons easier. 

Fig. 12 shows the curves of 8 subjects of all degrees of ultimate 
feeble-mindedness, who are arrested in mental age growth rel- 
atively early in life. The first I. Q.'s of two of these subjects 
are above 90. 13 Since we are dealing here with institutional sub- 
jects this is rather remarkable, though such types are undoubtedly 
not uncommon among ultimately feeble-minded children in the 
public schools. That they are not more frequently encountered 
is due to lack of early examining coupled with repeated tests.. 
All these 8 subjects show continuously decreasing I. Q.'s. The 
theory of a constant I. Q. requires that these subjects develop at 
rates varying from 25 to 93 until they are 16 years old, but as 
a matter of fact their net average rates are practically zero at 
10 years or earlier. 

Fig. 13 shows a series of 21 curves of subjects whose initial 
I. Q.'s are above 70 but whose net average rates of growth are 
below 50. These subjects are all gaining in mental age, but 
their net average gains are for the most part 50 per cent less than 
the rate predicted by the theory of a constant I. Q. Their I. Q.'s 
are therefore steadily decreasing. Nearly all of these subjects 
entirely cease to develop several years before age 16, the theo- 
retical limit to which they are expected to develop at a constant 
rate by the I. Q. 

Fig. 14 shows 3 subjects who reach points of arrest at 12 or 
13 years of age, but who prior to that point are developing at a 
net average rate which is 50 per cent greater than the rate ex- 
pected from the initial I. O. Their I. Q.'s are therefore steadily 
increasing. Finally, Fig. 15 shows three subjects whose net aver- 
age rate of growth corresponds approximately to the initial I. 

13 An I. Q. of 90 is ordinarily considered indicative of 'normal' intelli- 
gence as well as average intelligence. These subjects were diagnosed as 
potentially feeble-minded on the basis of clinical evidence which outweighed 
the 'at-ageness' of the Binet mental age score (cf. 8, 10, and 25). Subjects 
No. 134 and 164 have been fully reported in (8) pp. 90 to 140. 



THE GROWTH OF INTELLIGENCE 



109 




Age 7 



12 13 





Age 7 



Individual growth curves showing average rate of increase about half of 

initial I. Q. with consequent decrease in I. Q. values. 

Fig. 13 — Section A 



no 



EDGAR A. DOLL 




Age 




Age 7 




Fig. 13 — Section B 



THE GROWTH OF INTELLIGENCE 



in 




Age 8 




Age 8 



13 14 




Age 8 



9 10 11 12 13 

Fig. 13 — Section C 



14 



112 



EDGAR A. DOLL 






Age 9 10 11 12 13 

Fig. 13— Section D 



THE GROWTH OF INTELLIGENCE 



ii3 




Age 




10 





r <# 


7 

/ 
/ 

f 












V? 
















/ 




initi 


al I.C 


Case 
. 95; 


159 
eve. t 


ate 4( 




Rati' 


5 { 


I \ 


8 I 


8 ; 


I 







Age 8 9 10 11 ,12 

Fig. 13 — Section E 



13 



14 15 



U4 



EDGAR A. DOLL 




Age 10 




Age 10 



15 16 




Fig. 13 — Section F 



THE GROWTH OF INTELLIGENCE 



"5 




'Age 11 12 




'Age 11 



IT 



h* v 



£<- 



©8 " 



57 



Initi 



Case 
al I.C 



139 
, 78; 



ave. i ate 2! 



I.Q.' 

Rate 



78 



60 



71 

Uo 



€5 




€2 

El 



Age 10 11 12 13 14 

Fig. 13 — Section G 



15 16 



u6 



EDGAR A. DOLL 




e2« i^ueii 



THE GROWTH OF INTELLIGENCE 



ii7 




I Titian 



n8 EDGAR A. DOLL 

Q.'s. But two of these three reach a level of arrest at about 12 
years of age instead of 16. 

We may therefore conclude that only 1 subject out of a total 
of 106 feeble-minded subjects who were below 16 years of age 
at the first examination maintains an I. Q. which is in accord 
with the theory that the I. Q. is constant. In opposition to this 
theory we are obliged to conclude for the feeble-minded at least 
that there are as yet no obvious laws of mental age growth which 
can be made practical use of in predicting development in the 
individual feeble-minded subject. We must for the present con- 
tent ourselves with the general laws that, (1) there is an age 
of arrest for every feeble-minded subject which almost invari- 
ably is reached before 15 years of age, (2) that this age of ar- 
rest is a function of the final mental level, and (3) that the level 
is reached at a rate or growth which is a decreasing variable and 
is a function of life age. 

We have plotted only the growth curves of certain conspicuous 
types. In so doing we have justified the theoretical argument ad- 
vanced at the beginning of this report (cf. pp. 15 ft".). Other 
curves may be readily plotted from the data in Table 2, 

That these developmental types exist even in small numbers is 
a fact which cannot be ignored by clinical psychology. We agree 
with Dr. Mateer that mere 'at-ageness' in intelligence is not nec- 
essarily diagnostic of normality and even a few curves prove the 
point. The issue is clearly and forcefully presented by Dr. Ma- 
teer in the following paragraph (25, p. 391) : 

There is something more significant than mere mental age or years of re- 
tardation, a something we seem to have missed in our numerically finished 
clinical studies. At two an idiot, an imbecile, a moron and a normal may all 
seem practically the same. Then the idiot drops out of the race, stays at 
that level. Somewhere, in the next four or five years the imbecile falls be- 
hind, but the moron may be even ten or eleven before he evidences any real 
deficiency on our present system of tests. Yet the difference has been there 
all along. The moron was as feeble-minded, potentially, at the age of two, 
as at twelve. The normal child was as surely normal. There is an innate 
difference hard to describe, but all who know defective and normal children 
often recognize this qualitative difference before any quantitative test has 
demonstrated its presence. It seems as though with some the evolutionary 
nisus has spent itself with the effort necessary to bring into being, with 



THE GROWTH OF INTELLIGENCE 119 

others there is no energy there to meet the demand for speech, with others 
concrete stimuli can evoke satisfactory responses but there is not enough 
motive power to meet the demand for response to the faint stimulations made 
by abstract ideas, theories, principles, etc. But the normal child is entirely 
different. He lives only as an incarnation of activity, he is activity, innate, 
flooding, spilling with every new stimulus, responding with growth to every 
new demand made upon him. 

With respect to irregularities in the mental growth of indi- 
vidual superior children we may cite 5 cases from Terman (29, 
pp. 194 ff.), and 4 from the data supplied us by Miss Gil- 
lingham. The latter data are for subjects who have been ex- 
amined three times at intervals of from 1 to 2 years. We pre- 
sent the results in Table 15, showing the successive ages and 
mental ages for each subject, the increases in ages and mental 
ages, the I. Q.'s, the corresponding annual rates of growth, and 
the I. Q. changes. x 

The column headed 'Annual rate' shows marked irregu- 
larities in the same subject from year to year, varying in one 
subject from 370 per cent of the normal rate to 10 per cent. 
There are also> marked differences between the I. Q.'s as pre- 
dicted rates and the actual rates. The I. Q. changes are com- 
paratively slight, even when the differences between actual rates 
and predicted rates are very marked. As has already been 
pointed out, this is because the variation in rate is 'taken up' in 
the I. Q. change by being distributed over a period of years equal 
to the age of the subject. 

From all this evidence we may conclude that marked irregu- 
larities in the course of mental growth of subjects from year 
to year are actually present and easily observed. But these ir- 
regularities are obscured by the I. Q. mode of expressing mental 
growth, since the irregularities are smoothed in the I. Q. by be- 
ing distributed over a period of years. We may also note that 
these irregularities are not always in the same direction and 
therefore tend to compensate each other over periods of time 
which are longer than one or two years. But the irregularities 
are too large in amount to be traced to experimental variations 
in the conditions of obtaining mental age. In other words, the 
observed tendency of superior children to become still more su- 



120 EDGAR A. DOLL 

Table 15 

Irregular rates of mental age growth of superior children. 
Terman's cases 

Life Mental Annual 

Subject Life Mental age age rate of I. Q. 

No. ages ages I. Q.'s increases increases increase changes 
1 6.9 10.0 145 

7.9 13.2 167 1.0 3-2 320 +22 

IO.O l6.6 l66 2.1 3.4 162 — I 

4 4.6 6.7 145 

5.8 8.8 152 .8 2.1 262 +7 

7.0 10.7 153 1.2 1.9 158 + 1 

6 8.2 1 1.3 138 

1 1.0 15.2 138 2.8 3.9 139 o 
12.3 17.6 143 1-3 2.4 185 + 5 

17 3-2 4-7 147 

5.2 7.3 140 2.0 2.6 130 + 7 

6.3 8.8 140 1.1 1.5 136 o 

28 8.1 10.8 133 

9.2 13.0 141 1.1 2.2 200 -j- 8 

11.3 15-5 137 2.1 2.5 119 — 4 

Gillingham's Cases 
10.7 13.8 130 

11.7 17.5 150 1.0 3-7 37o +20 

12.7 17.6 139 1.0 .1 10 — 11 

11. 1 15.1 136 

12.2 16.0 131 1.1 .9 82 — s 

13.0 17.0 131 .8 1.0 125 o 

11.2 12.9 us 

12.1 13. 1 108 .9 .2 22 — 7 

13.2 15.8 120 1.1 2.7 246 -j-12 

1 1.4 12.8 112 

12.8 14.7 115 1-4 1-9 136 + 3 
13.8 16.3 118 1.0 1.6 160 +3 

perior is not regularly maintained from year to year for indi- 
vidual subjects although it has seemed to be a significant ten- 
dency from superior children on the average. 

The I. Q. and the scale of measurement. — Of course the con- 
stancy of the I. Q. will depend upon the accuracy of the mental 
age measuring scale. It will also be influenced by the care with 
which the exact life age is calculated and it will vary with such 
experimental conditions as Brigham (5) has so carefully in- 
vestigated. The 'completeness' or 'range' of examining in par- 



THE GROWTH OF INTELLIGENCE 121 

ticular will influence the I. Q., for if the first examination is not 
carried far enough into the upper ranges of the measuring scale 
this will exert a spurious influence. But in the long run the de- 
termination of the total mental age is fairly independent of these 
experimental variations, owing to compensating errors. 

It is possible, however, that the mental ages obtained by differ- 
ent measuring scales might yield different arguments concerning 
the I. Q. Terman has said (30, p. 104) : "It should be empha- 
sized, however, that what we have said about the significance 
of various I. Q.'s holds only for I. Q.'s secured by the use of the 
Stanford revision. As we have shown elsewhere (p. 62 ff.) the 
I. Q. yielded by other versions of the Binet tests are often so 
inaccurate as to be misleading." 

Our principal experimental evidence concerning the intelli- 
gence growth of feeble-minded subjects is based on the Goddard 
version of the Binet tests. Most of our references to the liter- 
ature are also based on authors who for the most part used the 
Goddard scale. Does this fact invalidate our argument? We 
think not and for the following reasons. 

We readily acknowledge that the Stanford revision is a much 
superior instrument to the Goddard scale. This is not, we be- 
lieve, due to the increased number of tests, selection of tests or 
to any fundamental difference in principles of standardization. 
It is due to greater care in the selection and examining of sub- 
jects on whom the Stanford Scale was standardized, and to 
greater care in the statistical treatment of standardization data. 
Another principal advantage, and one which is much more im- 
portant than the improved accuracy of standardizations is the 
extension of the Stanford Scale for the measurement of the 
higher mental ages. 

We have shown (cf. Fig. 4) that the Goddard Scale gives a 
close approximation of median mental age to median life age up 
to age 10, with minor inaccuracies not very much greater than 
those of the Stanford Revision (cf. Fig. 5). But a better dem- 
onstration of the superiority of the Stanford Scale is found in 
the calibration of the two scales. If we apply the method of 
Otis (27) to the two Scales, we find that whereas the Goddard 



122 EDGAR A. DOLL 

Scale is inaccurately calibrated with respect to the succession of 
tests, the Stanford Scale shows only minor inaccuracies of cali- 
bration. The principal inaccuracy of the Goddard Scale is be- 
tween 7 and 8 years. At other ages the standardization is fairly 
accurate. The writer has elsewhere shown (7) that this cali- 
bration is slightly different for feeble-minded subjects. It has 
also been pointed out that the Goddard Scale does not accurately 
measure mental ages higher than 10 years. With superior sub- 
jects its limit of efficiency is probably only 9 years. 

But none of these arguments seriously affects our results for 
the feeble-minded. The Scale is sufficiently extended for all but 
possibly the highest group of subjects, those whose final mental 
ages are 10 years. If we left out this group of subjects our con- 
clusions would not be materially affected. 

For the total range of the Goddard Scale we should have mat- 
ters somewhat as follows (cf. Fig. 4) : between 5 and 6 years a 
year's improvement in true mental age would register (on the 
average) as 1.6 years, between 6 and 7 as 1.1 years, between 7 
and 8 as .6 years, between 8 and 9 years as .5 years, between 9 
and 10 years as 1.2 years, and between 10 and 11 as 1.1 years. 
Therefore, when converting mental age increase to rates of de- 
velopment we ought not to have divided the actual gains by 1.0 
as the average annual rate of growth, but should have divided by 
1.6 at mental age 5, 1.1 at mental age 6, .6 at mental age 7, and 
so on. The serious changes would be at mental ages 5, 7 and 8. 
In other words, the 5-year-old, who is expected to gain only half 
a year from the tests beyond year V, actually gains a year, and 
so does the 6-year-old. This is because the Vl-year and VII- 
year tests are too easy. The 7-year-old finds the tests properly 
adjusted and 'tests' as he should, but the increase from age 6 to 
7 is only a half year because at age 6 the subject 'tested' too 
high. The 8-year-old, however, tests a half-year too low be- 
cause the VHI-year and IX-year tests are too hard for him, 
although a year later he finds them easy enough. In other words, 
as our calibration of the Goddard Scale shows, there will be ir- 
regularities in the mental growth rates at ages 5 to 6, 7 to 8, 
and 8 to* 9. 



THE GROWTH OF INTELLIGENCE 123 

But if this is true for the Goddard Scale it is also true for the 
Stanford Scale, though at different points (cf. Fig. 5). On the 
Stanford Scale the average child will gain 1.4 years between the 
ages of 4.5 and 5.5 and only .7 years between the ages of 5.5 
and 6.5. 

It appears, however, that the younger subjects of both God- 
dard and Terman were selected in favor of brightness. Hence 
the discrepancy at 5 and 6 years may be overlooked. The Stan- 
ford Scale then becomes a regular measure at all ages while the 
Goddard Scale is inaccurate only between 7 and 8 years. This 
is just what the Otis calibration of the Goddard Scale shows. 

The effect of this attenuation of the Goddard Scale is to cause 
an irregularity in rate of mental growth at about the age of 8 
years. The average normal rate of growth between 7.5 and 8.5 
years is only half of the theoretical standard rate of 100 per 
cent. 

The conclusion of this argument is, then, that when the God- 
dard Scale is applied to unselected average normal subjects whose 
mental ages are below 10 years, the rate of growth of unselected 
subjects will be approximately 100 for all ages except mental age 
7.5 to 8.5 years. Variations from the approximate standard of 
100 will be equally marked in the Stanford Scale except for this 
one year. 

This fact might be expected to influence our mental age curves 
(Fig. 10) at final mental ages 7 years, 8 years, or 9 years. In 
fact the growth curve for final mental age 9 is affected while pass- 
ing from 8 to 9 years. We cannot be sure that this is more than 
a coincidence, however, for the irregularity comes nearly a year 
later than one would expect from the theoretical considerations 
advanced above, which have indicated that these subjects should 
have met with difficulty in crossing the 8-year boundary rather 
than the 9-year boundary. 

Another course of argument might be carried out somewhat 
as follows. We may assume that the Stanford Scale is accept- 
ably accurate for measuring mental age. The relative accuracy 
of the Goddard Scale may then be determined in terms of the 
Stanford as a standard of comparison. Unfortunately we are 



124 



EDGAR A. DOLL 



unable to refer to any study of a large number of subjects ex- 
amined by both Scales. But in 1916 Miss Eleanor E. Gray, then 
a research assistant at the Training School, examined 82 insti- 
tutional feeble-minded subjects in this way. Both scales were 
employed at the same sitting for each subject, identical tests be- 
ing given only once and scored on both scales. Statistical treat- 
ment of these results gave a correlation of r = .98 for the exact 
comparative mental ages of the 74 subjects whose mental ages 
were below 11.0 by the Goddard Scale. The I. Q. correlation 
would be exactly the same, since for each subject the life age 
was the same for both mental ages. But this high correlation 
for the entire range of mental ages is somewhat misleading. 
The average results by separate mental ages are more striking. 
They are presented in Table 16. This table shows that the God- 

Table 16 

Comparison of mental ages obtained by examining the same feeble-minded 

subjects with the Goddard Binet and Stanford Binet Scales. 



Cental 










Annual 


Annual 


age 


No. 


Ave. M.A. 


Ave. M.A. 


Average 


increase 


increase 


group 


cases 


•Stanford 


Goddard 


difference 


Stanford Goddard 


2 


5 


2.72 


3-o8 


.36 






3 


5 


3-SO 


4.04 


•54 


•78 


.06 


4 


7 


4.44 


5-12 


.68 


•94 


1.08 


5 


6 


5.52 


6.37 


•85 


1.08 


1-25 


6 


8 


6.50 


7.40 


.00 


1.02 


1.03 


7 


7 


7-30 


7.83 


•53 


.80 


.63 


8 


8 


8.38 


8-75 


•37 


1.08 


.92 


9 


15 


9.60 


9-73 


•13 


1.22 


•98 


10 


10 


10.44 


10.36 


—.08 


.84 


.63 


11 


4 


11.45 


11.05 


—.40 


1. 01 


.69 


12 


5 


12.44 


10.92 


—1.48 


■99 


—.07 


13 


2 


13.40 


11.20 


— 2.20 


.96 


■32 



dard Scale yields higher mental ages at all stages up to mental 
age 10 years. This is another way of showing what we have 
already shown in the comparative calibrations of the scale, name- 
ly, that the Goddard Scale is comparatively easier than the Stan- 
ford Scale in the early mental ages, and is not an efficient meas- 
ure of mental age after 10 years. Up to mental age 8 years all 
but two subjects have higher mental ages by the Goddard Scale. 
ranging from a minimum of .1 years to a maximum of 1.3 years 
for individual subjects. At Stanford mental age 8 years, 60 per 
cent of individual mental ages are higher by the Goddard Scale, 
at 9 years 60 per cent, and at 10 years 30 per cent. 



THE GROWTH OF INTELLIGENCE 125 

The principal feature of comparison, however, is that the aver- 
age annual increases in mental age are much the same by both 
scales. While the comparative mental ages are different from 
year to year the comparative mental age increments are never 
greater than .2 years, that is are approximately the same for 
both scales from year to> year. Since in this study we are con- 
cerned primarily with mental age increases rather than with true 
mental ages, we may say that the measurement of mental growth 
for feeble-minded subjects under mental age 11 years is about as 
accurate by the Goddard Scale as by the Stanford Scale. The 
Stanford Scale is undoubtedly the more accurate scale for meas- 
uring actual mental age and should in future be used in pref- 
erence to the Goddard Scale. Nevertheless the Goddard Scale 
at its most inaccurate segments gives mental ages which do not 
differ as much as a year from those obtained by the Stanford 
Scale. It is almost exactly as accurate as the Stanford for 
measuring mental age increases. The comparative inaccuracy of 
the Goddard Scale is certainly not so great as to discredit our 
results for feeble-minded subjects on that basis. 

Still another argument to substantiate our use of the God- 
dard Scale is that although this scale may be irregular at certain 
points (which is true only in lesser degree of the Stanford Scale) 
it is not so irregular as to prevent the measurement of actual 
growth if the period of time is sufficiently extended or if the 
tendency to grow is sufficiently pronounced. We have shown 
that the greatest inhibition of mental age increase (by the God- 
dard Scale) among average normal subjects occurs at 8 years 
and that this temporary inhibition is later overcome by the 'facili- 
tated' or too easy mental age increase at other years. Hence the 
worst we could expect from an admittedly imperfect scale would 
be to find irregularities in our average growth curves (Fig. 10). 
This influence might also bring about a piling up of subjects at 
certain mental ages, such as mental age 5, which piling up ought 
to include some subjects whose 'true' final mental ages are only 
4 years. We ought also to find that those subjects whose ini- 
tial mental ages are about 4 years should make spurious gains, 
while those whose initial mental ages are about 7 years should 



126 EDGAR A. DOLL 

be spuriously arrested. These effects would only in part be ob- 
scured by our method of grouping according to final mental age. 

As a matter of fact we do find a slightly increased rate of 
growth between mental ages 4 and 5 years for those subjects 
whose final mental age is 6 years. And we do find a slight 
piling up of subjects at mental age 7 years. And it may be that 
the slope of our curve, for final mental age 8 years is unwar- 
rantedly flat. But these effects may just as well be the results 
of causes other than the irregularities of the scale, being caused 
possibly by the small numbers of subjects, the marked variations 
in the growth of individual subjects (which would be reflected in 
the small number of subjects), the accidental age-factor in the 
selection of subjects, and so on. Moreover, the effects noted in 
the curves are not exactly as predicted. The piling up of sub- 
jects should be in the 8-year group instead of the 7-year group, 
and the rapid rate of growth should be in the 5-year group in- 
stead of the 6-year group. And some subjects in each group 
are arrested while others advance in mental age. 

A large number of the subjects of our experimental study were 
examined by the Stanford Scale as well as by the Goddard Scale. 
Some were examined for several years by both scales. We have 
not been in a position to work up these results, but inspection of 
the data indicates that they would substantiate the above con- 
clusions. The Stanford mental age scores are usually a half 
year lower than the Goddard mental age scores, but the rates of 
increase by both scales are closely similar. In particular it can- 
not be said that the condition of potential feeble-mindedness is 
a reflection of an inadequate scale. The results of Dr. Mateer 
support our own evidence that sudden arrest in mental develop- 
ment is equally obvious by either scale. 

From all these considerations we may conclude that the God- 
dard Scale is a valid scale for our purposes no matter from what 
angle it is viewed. The argument is of course crucial to the 
validity of our conclusions with respect to the feeble-minded. 
Our other results are above reproach in these respects, being 
based on the Stanford Scale. 



IV. SUMMARY AND CONCLUSIONS 

1. Intelligence is defined in this study in terms of its essential 
activities : judgment, comprehension and reasoning. The growth 
of intelligence is here measured by comparing successive Binet 
mental ages of the same individuals obtained by repeated exami- 
nations over long periods of time. 

2. The accepted theoretical curve of average normal growth of 
intelligence misrepresents the probable facts. Logical consider- 
ations and the facts of child study suggest significant modifica- 
tions of the theoretical curve of growth which is commonly ac- 
cepted in the psychology of intellectual development. For prac- 
tical purposes an empirical straight-line curve of average normal 
growth in terms of relative units of mental age may be employed 
as a standard of comparison. 

3. The experimental proof is inadequate regarding the mental 
age which shall be accepted as representing average normal adult 
intelligence. The most recent and extensive evidence suggests 
that the average adult level of intelligence is between 13 and 14 
years instead of being 16 years as has been recently accepted in 
the field of clinical psychology. The final disposition of this 
question is complicated by the difficulty of obtaining representa- 
tive unselected subjects in the higher life ages. 

4. Repeated Binet tests almost inevitably show an error of 
incomplete examining. To correct this error a set of objective 
rules are developed to supply scores for single test-scores which 
may have been omitted from an examination. 

5. When the growth of intelligence of feeble-minded subjects 
is experimentally investigated by comparing successive mental 
age increases as a result of repeated examinations of the same 
subjects, the following 'laws' of growth are established: 

a. Significant mental age increases are limited to subjects un- 
der 15 years of life age. 

b. The age of final mental arrest is determined in largest 
measure by the final mental age level (hereditarily predeter- 
mined?) and cannot be predicted from a given mental age or a 
given degree of mental retardation such as may be evident from 



128 EDGAR A. DOLL 

one or several examinations early in life by any present device 
for expressing intellectual development. 

c. The rate of intellectual development is a function of the 
life age of the individual subject. It is relatively independent of 
the final mental level or an initial degree of retardation. 

d. The average annual rate of growth is relatively independent 
of the contemporary mental age level. It decreases by increasing 
amounts as life age increases. It reaches a minimum at about 13 
years of life age. 

6. The rate of growth of superior children between the ages 
of 9 and 13 years life age is negatively correlated with mental 
age and degree of brightness. Individual variability in the rates 
of intellectual growth of superior children is very marked. 

7. No conclusion is established regarding the age of arrest of 
intellectual growth among superior children. 

8. The conclusions established by this experimental investiga- 
tion are in harmony with theoretical expectation founded on ob- 
servation and the known facts of intellectual growth. 

9. The contention of several authorities that the intelligence 
quotient is approximately constant between the ages of 4 and 16 
years of life age for all degrees of brightness is not justified 
either by theoretical considerations or by the experimental evi- 
dence now available in the literature of the subject. 

10. 'Approximateness' of I. Q.'s may be expressed numerically. 
When this is done it is evident that equal rates of annual growth 
yield markedly different degrees of approximateness at differ- 
ent ages. 

11. The I. Q. instead of being approximately constant is 
markedly variable in individual cases. The likelihood of an I. Q v 
remaining approximately constant can be expressed in terms of 
probability with a fair degree of accuracy. Except in this way 
no single I. Q. can safely be used as a means of predicting indi- 
vidual mental age growth with certainty or accuracy. 

12. Marked irregularities in the rates of growth of intelligence 
among individual children of feeble-minded, borderline, and su- 
perior children are demonstrated by growth curves covering long 
periods of time. The data are insufficient to indicate the periods 
at which intellectual growth is retarded or accelerated. 



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